get_coeff.m

function [coefot coef1t coef2t coef3t coef4t coef5t ] = get_coeff( x0,x1,x2,x3,x4,x5,t0,t,tf )

%% --get coefot %%%%%%
coefot=-(1/((t0-tf)^10))*5*(-(t^10/10)+t0^10/10+t^9*tf-t0^9*tf-(9*t^8*tf^2)/2+(9*t0^8*tf^2)/2+12*t^7*tf^3-12*t0^7*tf^3-21*t^6*tf^4+21*t0^6*tf^4+(126*t^5*tf^5)/5-(126*t0^5*tf^5)/5-21*t^4*tf^6+21*t0^4*tf^6+12*t^3*tf^7-12*t0^3*tf^7-(9*t^2*tf^8)/2+(9*t0^2*tf^8)/2+t*tf^9-t0*tf^9)*x0-(1/((t0-tf)^10))*5*(t^10/2-(4*t^9*t0)/9-t0^10/18-(41*t^9*tf)/9+4*t^8*t0*tf+(5*t0^9*tf)/9+(37*t^8*tf^2)/2-16*t^7*t0*tf^2-(5*t0^8*tf^2)/2-44*t^7*tf^3+112/3*t^6*t0*tf^3+(20*t0^7*tf^3)/3+(203*t^6*tf^4)/3-56*t^5*t0*tf^4-(35*t0^6*tf^4)/3-70*t^5*tf^5+56*t^4*t0*tf^5+14*t0^5*tf^5+49*t^4*tf^6-112/3*t^3*t0*tf^6-(35*t0^4*tf^6)/3-(68*t^3*tf^7)/3+16*t^2*t0*tf^7+(20*t0^3*tf^7)/3+(13*t^2*tf^8)/2-4*t*t0*tf^8-(5*t0^2*tf^8)/2-t*tf^9+t0*tf^9)*x1-(1/((t0-tf)^10))*5*(-t^10+(16*t^9*t0)/9-(3*t^8*t0^2)/4-t0^10/36+(74*t^9*tf)/9-29/2*t^8*t0*tf+6*t^7*t0^2*tf+(5*t0^9*tf)/18-(119*t^8*tf^2)/4+52*t^7*t0*tf^2-21*t^6*t0^2*tf^2-(5*t0^8*tf^2)/4+62*t^7*tf^3-322/3*t^6*t0*tf^3+42*t^5*t0^2*tf^3+(10*t0^7*tf^3)/3-(245*t^6*tf^4)/3+140*t^5*t0*tf^4-105/2*t^4*t0^2*tf^4-(35*t0^6*tf^4)/6+70*t^5*tf^5-119*t^4*t0*tf^5+42*t^3*t0^2*tf^5+7*t0^5*tf^5-(77*t^4*tf^6)/2+196/3*t^3*t0*tf^6-21*t^2*t0^2*tf^6-(35*t0^4*tf^6)/6+(38*t^3*tf^7)/3-22*t^2*t0*tf^7+6*t*t0^2*tf^7+(10*t0^3*tf^7)/3-2*t^2*tf^8+4*t*t0*tf^8-2*t0^2*tf^8)*x2-(1/((t0-tf)^10))*5*(t^10-(8*t^9*t0)/3+(9*t^8*t0^2)/4-(4*t^7*t0^3)/7-t0^10/84-(22*t^9*tf)/3+39/2*t^8*t0*tf-114/7*t^7*t0^2*tf+4*t^6*t0^3*tf+(5*t0^9*tf)/42+(93*t^8*tf^2)/4-432/7*t^7*t0*tf^2+51*t^6*t0^2*tf^2-12*t^5*t0^3*tf^2-(15*t0^8*tf^2)/28-(290*t^7*tf^3)/7+110*t^6*t0*tf^3-90*t^5*t0^2*tf^3+20*t^4*t0^3*tf^3+(10*t0^7*tf^3)/7+45*t^6*tf^4-120*t^5*t0*tf^4+195/2*t^4*t0^2*tf^4-20*t^3*t0^3*tf^4-(5*t0^6*tf^4)/2-30*t^5*tf^5+81*t^4*t0*tf^5-66*t^3*t0^2*tf^5+12*t^2*t0^3*tf^5+3*t0^5*tf^5+(23*t^4*tf^6)/2-32*t^3*t0*tf^6+27*t^2*t0^2*tf^6-4*t*t0^3*tf^6-(5*t0^4*tf^6)/2-2*t^3*tf^7+6*t^2*t0*tf^7-6*t*t0^2*tf^7+2*t0^3*tf^7)*x3-(1/((t0-tf)^10))*5*(-(t^10/2)+(16*t^9*t0)/9-(9*t^8*t0^2)/4+(8*t^7*t0^3)/7-(t^6*t0^4)/6-t0^10/252+(29*t^9*tf)/9-23/2*t^8*t0*tf+102/7*t^7*t0^2*tf-22/3*t^6*t0^3*tf+t^5*t0^4*tf+(5*t0^9*tf)/126-(35*t^8*tf^2)/4+220/7*t^7*t0*tf^2-40*t^6*t0^2*tf^2+20*t^5*t0^3*tf^2-5/2*t^4*t0^4*tf^2-(5*t0^8*tf^2)/28+(90*t^7*tf^3)/7-140/3*t^6*t0*tf^3+60*t^5*t0^2*tf^3-30*t^4*t0^3*tf^3+10/3*t^3*t0^4*tf^3+(10*t0^7*tf^3)/21-(65*t^6*tf^4)/6+40*t^5*t0*tf^4-105/2*t^4*t0^2*tf^4+80/3*t^3*t0^3*tf^4-5/2*t^2*t0^4*tf^4-(5*t0^6*tf^4)/6+5*t^5*tf^5-19*t^4*t0*tf^5+26*t^3*t0^2*tf^5-14*t^2*t0^3*tf^5+t*t0^4*tf^5+t0^5*tf^5-t^4*tf^6+4*t^3*t0*tf^6-6*t^2*t0^2*tf^6+4*t*t0^3*tf^6-t0^4*tf^6)*x4-(1/((t0-tf)^10))*5*(t^10/10-(4*t^9*t0)/9+(3*t^8*t0^2)/4-(4*t^7*t0^3)/7+(t^6*t0^4)/6-t0^10/1260-(5*t^9*tf)/9+5/2*t^8*t0*tf-30/7*t^7*t0^2*tf+10/3*t^6*t0^3*tf-t^5*t0^4*tf+(t0^9*tf)/126+(5*t^8*tf^2)/4-40/7*t^7*t0*tf^2+10*t^6*t0^2*tf^2-8*t^5*t0^3*tf^2+5/2*t^4*t0^4*tf^2-(t0^8*tf^2)/28-(10*t^7*tf^3)/7+20/3*t^6*t0*tf^3-12*t^5*t0^2*tf^3+10*t^4*t0^3*tf^3-10/3*t^3*t0^4*tf^3+(2*t0^7*tf^3)/21+(5*t^6*tf^4)/6-4*t^5*t0*tf^4+15/2*t^4*t0^2*tf^4-20/3*t^3*t0^3*tf^4+5/2*t^2*t0^4*tf^4-(t0^6*tf^4)/6-(t^5*tf^5)/5+t^4*t0*tf^5-2*t^3*t0^2*tf^5+2*t^2*t0^3*tf^5-t*t0^4*tf^5+(t0^5*tf^5)/5)*x5;
     %% --get coef1t %%%%%%
 coef1t=-(1/((t0-tf)^10))*5*(t^10/2-(5*t^9*t0)/9+t0^10/18-(40*t^9*tf)/9+5*t^8*t0*tf-(5*t0^9*tf)/9+(35*t^8*tf^2)/2-20*t^7*t0*tf^2+(5*t0^8*tf^2)/2-40*t^7*tf^3+140/3*t^6*t0*tf^3-(20*t0^7*tf^3)/3+(175*t^6*tf^4)/3-70*t^5*t0*tf^4+(35*t0^6*tf^4)/3-56*t^5*tf^5+70*t^4*t0*tf^5-14*t0^5*tf^5+35*t^4*tf^6-140/3*t^3*t0*tf^6+(35*t0^4*tf^6)/3-(40*t^3*tf^7)/3+20*t^2*t0*tf^7-(20*t0^3*tf^7)/3+(5*t^2*tf^8)/2-5*t*t0*tf^8+(5*t0^2*tf^8)/2)*x0-(1/((t0-tf)^10))*5*(-((5*t^10)/2)+5*t^9*t0-(5*t^8*t0^2)/2+20*t^9*tf-40*t^8*t0*tf+20*t^7*t0^2*tf-70*t^8*tf^2+140*t^7*t0*tf^2-70*t^6*t0^2*tf^2+140*t^7*tf^3-280*t^6*t0*tf^3+140*t^5*t0^2*tf^3-175*t^6*tf^4+350*t^5*t0*tf^4-175*t^4*t0^2*tf^4+140*t^5*tf^5-280*t^4*t0*tf^5+140*t^3*t0^2*tf^5-70*t^4*tf^6+140*t^3*t0*tf^6-70*t^2*t0^2*tf^6+20*t^3*tf^7-40*t^2*t0*tf^7+20*t*t0^2*tf^7-(5*t^2*tf^8)/2+5*t*t0*tf^8-(5*t0^2*tf^8)/2)*x1-(1/((t0-tf)^10))*5*(5*t^10-(130*t^9*t0)/9+(55*t^8*t0^2)/4-(30*t^7*t0^3)/7-(5*t0^10)/252-(320*t^9*tf)/9+205/2*t^8*t0*tf-680/7*t^7*t0^2*tf+30*t^6*t0^3*tf+(25*t0^9*tf)/126+(435*t^8*tf^2)/4-2190/7*t^7*t0*tf^2+295*t^6*t0^2*tf^2-90*t^5*t0^3*tf^2-(25*t0^8*tf^2)/28-(1300*t^7*tf^3)/7+1600/3*t^6*t0*tf^3-500*t^5*t0^2*tf^3+150*t^4*t0^3*tf^3+(50*t0^7*tf^3)/21+(575*t^6*tf^4)/3-550*t^5*t0*tf^4+1025/2*t^4*t0^2*tf^4-150*t^3*t0^3*tf^4-(25*t0^6*tf^4)/6-120*t^5*tf^5+345*t^4*t0*tf^5-320*t^3*t0^2*tf^5+90*t^2*t0^3*tf^5+5*t0^5*tf^5+(85*t^4*tf^6)/2-370/3*t^3*t0*tf^6+115*t^2*t0^2*tf^6-30*t*t0^3*tf^6-(25*t0^4*tf^6)/6-(20*t^3*tf^7)/3+20*t^2*t0*tf^7-20*t*t0^2*tf^7+(20*t0^3*tf^7)/3)*x2-(1/((t0-tf)^10))*5*(-5*t^10+(170*t^9*t0)/9-(105*t^8*t0^2)/4+(110*t^7*t0^3)/7-(10*t^6*t0^4)/3-(5*t0^10)/252+(280*t^9*tf)/9-235/2*t^8*t0*tf+1140/7*t^7*t0^2*tf-290/3*t^6*t0^3*tf+20*t^5*t0^4*tf+(25*t0^9*tf)/126-(325*t^8*tf^2)/4+2150/7*t^7*t0*tf^2-425*t^6*t0^2*tf^2+250*t^5*t0^3*tf^2-50*t^4*t0^4*tf^2-(25*t0^8*tf^2)/28+(800*t^7*tf^3)/7-1300/3*t^6*t0*tf^3+600*t^5*t0^2*tf^3-350*t^4*t0^3*tf^3+200/3*t^3*t0^4*tf^3+(50*t0^7*tf^3)/21-(275*t^6*tf^4)/3+350*t^5*t0*tf^4-975/2*t^4*t0^2*tf^4+850/3*t^3*t0^3*tf^4-50*t^2*t0^4*tf^4-(25*t0^6*tf^4)/6+40*t^5*tf^5-155*t^4*t0*tf^5+220*t^3*t0^2*tf^5-130*t^2*t0^3*tf^5+20*t*t0^4*tf^5+5*t0^5*tf^5-(15*t^4*tf^6)/2+30*t^3*t0*tf^6-45*t^2*t0^2*tf^6+30*t*t0^3*tf^6-(15*t0^4*tf^6)/2)*x3-(1/((t0-tf)^10))*5*((5*t^10)/2-(35*t^9*t0)/3+(85*t^8*t0^2)/4-(130*t^7*t0^3)/7+(15*t^6*t0^4)/2-t^5*t0^5-t0^10/84-(40*t^9*tf)/3+125/2*t^8*t0*tf-800/7*t^7*t0^2*tf+100*t^6*t0^3*tf-40*t^5*t0^4*tf+5*t^4*t0^5*tf+(5*t0^9*tf)/42+(115*t^8*tf^2)/4-950/7*t^7*t0*tf^2+250*t^6*t0^2*tf^2-220*t^5*t0^3*tf^2+175/2*t^4*t0^4*tf^2-10*t^3*t0^5*tf^2-(15*t0^8*tf^2)/28-(220*t^7*tf^3)/7+150*t^6*t0*tf^3-280*t^5*t0^2*tf^3+250*t^4*t0^3*tf^3-100*t^3*t0^4*tf^3+10*t^2*t0^5*tf^3+(10*t0^7*tf^3)/7+(35*t^6*tf^4)/2-85*t^5*t0*tf^4+325/2*t^4*t0^2*tf^4-150*t^3*t0^3*tf^4+125/2*t^2*t0^4*tf^4-5*t*t0^5*tf^4-(5*t0^6*tf^4)/2-4*t^5*tf^5+20*t^4*t0*tf^5-40*t^3*t0^2*tf^5+40*t^2*t0^3*tf^5-20*t*t0^4*tf^5+4*t0^5*tf^5)*x4-(1/((t0-tf)^10))*5*(-(t^10/2)+(25*t^9*t0)/9-(25*t^8*t0^2)/4+(50*t^7*t0^3)/7-(25*t^6*t0^4)/6+t^5*t0^5-t0^10/252+(20*t^9*tf)/9-25/2*t^8*t0*tf+200/7*t^7*t0^2*tf-100/3*t^6*t0^3*tf+20*t^5*t0^4*tf-5*t^4*t0^5*tf+(5*t0^9*tf)/126-(15*t^8*tf^2)/4+150/7*t^7*t0*tf^2-50*t^6*t0^2*tf^2+60*t^5*t0^3*tf^2-75/2*t^4*t0^4*tf^2+10*t^3*t0^5*tf^2-(5*t0^8*tf^2)/28+(20*t^7*tf^3)/7-50/3*t^6*t0*tf^3+40*t^5*t0^2*tf^3-50*t^4*t0^3*tf^3+100/3*t^3*t0^4*tf^3-10*t^2*t0^5*tf^3+(10*t0^7*tf^3)/21-(5*t^6*tf^4)/6+5*t^5*t0*tf^4-25/2*t^4*t0^2*tf^4+50/3*t^3*t0^3*tf^4-25/2*t^2*t0^4*tf^4+5*t*t0^5*tf^4-(5*t0^6*tf^4)/6)*x5;
 %% --get coef2t %%%%%%
 coef2t=-(1/((t0-tf)^10))*5*(-t^10+(20*t^9*t0)/9-(5*t^8*t0^2)/4+t0^10/36+(70*t^9*tf)/9-35/2*t^8*t0*tf+10*t^7*t0^2*tf-(5*t0^9*tf)/18-(105*t^8*tf^2)/4+60*t^7*t0*tf^2-35*t^6*t0^2*tf^2+(5*t0^8*tf^2)/4+50*t^7*tf^3-350/3*t^6*t0*tf^3+70*t^5*t0^2*tf^3-(10*t0^7*tf^3)/3-(175*t^6*tf^4)/3+140*t^5*t0*tf^4-175/2*t^4*t0^2*tf^4+(35*t0^6*tf^4)/6+42*t^5*tf^5-105*t^4*t0*tf^5+70*t^3*t0^2*tf^5-7*t0^5*tf^5-(35*t^4*tf^6)/2+140/3*t^3*t0*tf^6-35*t^2*t0^2*tf^6+(35*t0^4*tf^6)/6+(10*t^3*tf^7)/3-10*t^2*t0*tf^7+10*t*t0^2*tf^7-(10*t0^3*tf^7)/3)*x0-(1/((t0-tf)^10))*5*(5*t^10-(140*t^9*t0)/9+(65*t^8*t0^2)/4-(40*t^7*t0^3)/7+(5*t0^10)/252-(310*t^9*tf)/9+215/2*t^8*t0*tf-790/7*t^7*t0^2*tf+40*t^6*t0^3*tf-(25*t0^9*tf)/126+(405*t^8*tf^2)/4-2220/7*t^7*t0*tf^2+335*t^6*t0^2*tf^2-120*t^5*t0^3*tf^2+(25*t0^8*tf^2)/28-(1150*t^7*tf^3)/7+1550/3*t^6*t0*tf^3-550*t^5*t0^2*tf^3+200*t^4*t0^3*tf^3-(50*t0^7*tf^3)/21+(475*t^6*tf^4)/3-500*t^5*t0*tf^4+1075/2*t^4*t0^2*tf^4-200*t^3*t0^3*tf^4+(25*t0^6*tf^4)/6-90*t^5*tf^5+285*t^4*t0*tf^5-310*t^3*t0^2*tf^5+120*t^2*t0^3*tf^5-5*t0^5*tf^5+(55*t^4*tf^6)/2-260/3*t^3*t0*tf^6+95*t^2*t0^2*tf^6-40*t*t0^3*tf^6+(25*t0^4*tf^6)/6-(10*t^3*tf^7)/3+10*t^2*t0*tf^7-10*t*t0^2*tf^7+(10*t0^3*tf^7)/3)*x1-(1/((t0-tf)^10))*5*(-10*t^10+40*t^9*t0-60*t^8*t0^2+40*t^7*t0^3-10*t^6*t0^4+60*t^9*tf-240*t^8*t0*tf+360*t^7*t0^2*tf-240*t^6*t0^3*tf+60*t^5*t0^4*tf-150*t^8*tf^2+600*t^7*t0*tf^2-900*t^6*t0^2*tf^2+600*t^5*t0^3*tf^2-150*t^4*t0^4*tf^2+200*t^7*tf^3-800*t^6*t0*tf^3+1200*t^5*t0^2*tf^3-800*t^4*t0^3*tf^3+200*t^3*t0^4*tf^3-150*t^6*tf^4+600*t^5*t0*tf^4-900*t^4*t0^2*tf^4+600*t^3*t0^3*tf^4-150*t^2*t0^4*tf^4+60*t^5*tf^5-240*t^4*t0*tf^5+360*t^3*t0^2*tf^5-240*t^2*t0^3*tf^5+60*t*t0^4*tf^5-10*t^4*tf^6+40*t^3*t0*tf^6-60*t^2*t0^2*tf^6+40*t*t0^3*tf^6-10*t0^4*tf^6)*x2-(1/((t0-tf)^10))*5*(10*t^10-(440*t^9*t0)/9+95*t^8*t0^2-(640*t^7*t0^3)/7+(130*t^6*t0^4)/3-8*t^5*t0^5-t0^10/63-(460*t^9*tf)/9+250*t^8*t0*tf-3400/7*t^7*t0^2*tf+1400/3*t^6*t0^3*tf-220*t^5*t0^4*tf+40*t^4*t0^5*tf+(10*t0^9*tf)/63+105*t^8*tf^2-3600/7*t^7*t0*tf^2+1000*t^6*t0^2*tf^2-960*t^5*t0^3*tf^2+450*t^4*t0^4*tf^2-80*t^3*t0^5*tf^2-(5*t0^8*tf^2)/7-(760*t^7*tf^3)/7+1600/3*t^6*t0*tf^3-1040*t^5*t0^2*tf^3+1000*t^4*t0^3*tf^3-1400/3*t^3*t0^4*tf^3+80*t^2*t0^5*tf^3+(40*t0^7*tf^3)/21+(170*t^6*tf^4)/3-280*t^5*t0*tf^4+550*t^4*t0^2*tf^4-1600/3*t^3*t0^3*tf^4+250*t^2*t0^4*tf^4-40*t*t0^5*tf^4-(10*t0^6*tf^4)/3-12*t^5*tf^5+60*t^4*t0*tf^5-120*t^3*t0^2*tf^5+120*t^2*t0^3*tf^5-60*t*t0^4*tf^5+12*t0^5*tf^5)*x3-(1/((t0-tf)^10))*5*(-5*t^10+(260*t^9*t0)/9-(275*t^8*t0^2)/4+(600*t^7*t0^3)/7-(175*t^6*t0^4)/3+20*t^5*t0^5-(5*t^4*t0^6)/2-(5*t0^10)/252+(190*t^9*tf)/9-245/2*t^8*t0*tf+2050/7*t^7*t0^2*tf-1100/3*t^6*t0^3*tf+250*t^5*t0^4*tf-85*t^4*t0^5*tf+10*t^3*t0^6*tf+(25*t0^9*tf)/126-(135*t^8*tf^2)/4+1380/7*t^7*t0*tf^2-475*t^6*t0^2*tf^2+600*t^5*t0^3*tf^2-825/2*t^4*t0^4*tf^2+140*t^3*t0^5*tf^2-15*t^2*t0^6*tf^2-(25*t0^8*tf^2)/28+(170*t^7*tf^3)/7-430/3*t^6*t0*tf^3+350*t^5*t0^2*tf^3-450*t^4*t0^3*tf^3+950/3*t^3*t0^4*tf^3-110*t^2*t0^5*tf^3+10*t*t0^6*tf^3+(50*t0^7*tf^3)/21-(20*t^6*tf^4)/3+40*t^5*t0*tf^4-100*t^4*t0^2*tf^4+400/3*t^3*t0^3*tf^4-100*t^2*t0^4*tf^4+40*t*t0^5*tf^4-(20*t0^6*tf^4)/3)*x4-(1/((t0-tf)^10))*5*(t^10-(20*t^9*t0)/3+(75*t^8*t0^2)/4-(200*t^7*t0^3)/7+25*t^6*t0^4-12*t^5*t0^5+(5*t^4*t0^6)/2-t0^10/84-(10*t^9*tf)/3+45/2*t^8*t0*tf-450/7*t^7*t0^2*tf+100*t^6*t0^3*tf-90*t^5*t0^4*tf+45*t^4*t0^5*tf-10*t^3*t0^6*tf+(5*t0^9*tf)/42+(15*t^8*tf^2)/4-180/7*t^7*t0*tf^2+75*t^6*t0^2*tf^2-120*t^5*t0^3*tf^2+225/2*t^4*t0^4*tf^2-60*t^3*t0^5*tf^2+15*t^2*t0^6*tf^2-(15*t0^8*tf^2)/28-(10*t^7*tf^3)/7+10*t^6*t0*tf^3-30*t^5*t0^2*tf^3+50*t^4*t0^3*tf^3-50*t^3*t0^4*tf^3+30*t^2*t0^5*tf^3-10*t*t0^6*tf^3+(10*t0^7*tf^3)/7)*x5;
 
 %% get coef3t %%%%%%%%
  coef3t= -(1/((t0-tf)^10))*5*(t^10-(10*t^9*t0)/3+(15*t^8*t0^2)/4-(10*t^7*t0^3)/7+t0^10/84-(20*t^9*tf)/3+45/2*t^8*t0*tf-180/7*t^7*t0^2*tf+10*t^6*t0^3*tf-(5*t0^9*tf)/42+(75*t^8*tf^2)/4-450/7*t^7*t0*tf^2+75*t^6*t0^2*tf^2-30*t^5*t0^3*tf^2+(15*t0^8*tf^2)/28-(200*t^7*tf^3)/7+100*t^6*t0*tf^3-120*t^5*t0^2*tf^3+50*t^4*t0^3*tf^3-(10*t0^7*tf^3)/7+25*t^6*tf^4-90*t^5*t0*tf^4+225/2*t^4*t0^2*tf^4-50*t^3*t0^3*tf^4+(5*t0^6*tf^4)/2-12*t^5*tf^5+45*t^4*t0*tf^5-60*t^3*t0^2*tf^5+30*t^2*t0^3*tf^5-3*t0^5*tf^5+(5*t^4*tf^6)/2-10*t^3*t0*tf^6+15*t^2*t0^2*tf^6-10*t*t0^3*tf^6+(5*t0^4*tf^6)/2)*x0-(1/((t0-tf)^10))*5*(-5*t^10+(190*t^9*t0)/9-(135*t^8*t0^2)/4+(170*t^7*t0^3)/7-(20*t^6*t0^4)/3+(5*t0^10)/252+(260*t^9*tf)/9-245/2*t^8*t0*tf+1380/7*t^7*t0^2*tf-430/3*t^6*t0^3*tf+40*t^5*t0^4*tf-(25*t0^9*tf)/126-(275*t^8*tf^2)/4+2050/7*t^7*t0*tf^2-475*t^6*t0^2*tf^2+350*t^5*t0^3*tf^2-100*t^4*t0^4*tf^2+(25*t0^8*tf^2)/28+(600*t^7*tf^3)/7-1100/3*t^6*t0*tf^3+600*t^5*t0^2*tf^3-450*t^4*t0^3*tf^3+400/3*t^3*t0^4*tf^3-(50*t0^7*tf^3)/21-(175*t^6*tf^4)/3+250*t^5*t0*tf^4-825/2*t^4*t0^2*tf^4+950/3*t^3*t0^3*tf^4-100*t^2*t0^4*tf^4+(25*t0^6*tf^4)/6+20*t^5*tf^5-85*t^4*t0*tf^5+140*t^3*t0^2*tf^5-110*t^2*t0^3*tf^5+40*t*t0^4*tf^5-5*t0^5*tf^5-(5*t^4*tf^6)/2+10*t^3*t0*tf^6-15*t^2*t0^2*tf^6+10*t*t0^3*tf^6-(5*t0^4*tf^6)/2)*x1-(1/((t0-tf)^10))*5*(10*t^10-(460*t^9*t0)/9+105*t^8*t0^2-(760*t^7*t0^3)/7+(170*t^6*t0^4)/3-12*t^5*t0^5+t0^10/63-(440*t^9*tf)/9+250*t^8*t0*tf-3600/7*t^7*t0^2*tf+1600/3*t^6*t0^3*tf-280*t^5*t0^4*tf+60*t^4*t0^5*tf-(10*t0^9*tf)/63+95*t^8*tf^2-3400/7*t^7*t0*tf^2+1000*t^6*t0^2*tf^2-1040*t^5*t0^3*tf^2+550*t^4*t0^4*tf^2-120*t^3*t0^5*tf^2+(5*t0^8*tf^2)/7-(640*t^7*tf^3)/7+1400/3*t^6*t0*tf^3-960*t^5*t0^2*tf^3+1000*t^4*t0^3*tf^3-1600/3*t^3*t0^4*tf^3+120*t^2*t0^5*tf^3-(40*t0^7*tf^3)/21+(130*t^6*tf^4)/3-220*t^5*t0*tf^4+450*t^4*t0^2*tf^4-1400/3*t^3*t0^3*tf^4+250*t^2*t0^4*tf^4-60*t*t0^5*tf^4+(10*t0^6*tf^4)/3-8*t^5*tf^5+40*t^4*t0*tf^5-80*t^3*t0^2*tf^5+80*t^2*t0^3*tf^5-40*t*t0^4*tf^5+8*t0^5*tf^5)*x2-(1/((t0-tf)^10))*5*(-10*t^10+60*t^9*t0-150*t^8*t0^2+200*t^7*t0^3-150*t^6*t0^4+60*t^5*t0^5-10*t^4*t0^6+40*t^9*tf-240*t^8*t0*tf+600*t^7*t0^2*tf-800*t^6*t0^3*tf+600*t^5*t0^4*tf-240*t^4*t0^5*tf+40*t^3*t0^6*tf-60*t^8*tf^2+360*t^7*t0*tf^2-900*t^6*t0^2*tf^2+1200*t^5*t0^3*tf^2-900*t^4*t0^4*tf^2+360*t^3*t0^5*tf^2-60*t^2*t0^6*tf^2+40*t^7*tf^3-240*t^6*t0*tf^3+600*t^5*t0^2*tf^3-800*t^4*t0^3*tf^3+600*t^3*t0^4*tf^3-240*t^2*t0^5*tf^3+40*t*t0^6*tf^3-10*t^6*tf^4+60*t^5*t0*tf^4-150*t^4*t0^2*tf^4+200*t^3*t0^3*tf^4-150*t^2*t0^4*tf^4+60*t*t0^5*tf^4-10*t0^6*tf^4)*x3-(1/((t0-tf)^10))*5*(5*t^10-(310*t^9*t0)/9+(405*t^8*t0^2)/4-(1150*t^7*t0^3)/7+(475*t^6*t0^4)/3-90*t^5*t0^5+(55*t^4*t0^6)/2-(10*t^3*t0^7)/3-(5*t0^10)/252-(140*t^9*tf)/9+215/2*t^8*t0*tf-2220/7*t^7*t0^2*tf+1550/3*t^6*t0^3*tf-500*t^5*t0^4*tf+285*t^4*t0^5*tf-260/3*t^3*t0^6*tf+10*t^2*t0^7*tf+(25*t0^9*tf)/126+(65*t^8*tf^2)/4-790/7*t^7*t0*tf^2+335*t^6*t0^2*tf^2-550*t^5*t0^3*tf^2+1075/2*t^4*t0^4*tf^2-310*t^3*t0^5*tf^2+95*t^2*t0^6*tf^2-10*t*t0^7*tf^2-(25*t0^8*tf^2)/28-(40*t^7*tf^3)/7+40*t^6*t0*tf^3-120*t^5*t0^2*tf^3+200*t^4*t0^3*tf^3-200*t^3*t0^4*tf^3+120*t^2*t0^5*tf^3-40*t*t0^6*tf^3+(40*t0^7*tf^3)/7)*x4-(1/((t0-tf)^10))*5*(-t^10+(70*t^9*t0)/9-(105*t^8*t0^2)/4+50*t^7*t0^3-(175*t^6*t0^4)/3+42*t^5*t0^5-(35*t^4*t0^6)/2+(10*t^3*t0^7)/3-t0^10/36+(20*t^9*tf)/9-35/2*t^8*t0*tf+60*t^7*t0^2*tf-350/3*t^6*t0^3*tf+140*t^5*t0^4*tf-105*t^4*t0^5*tf+140/3*t^3*t0^6*tf-10*t^2*t0^7*tf+(5*t0^9*tf)/18-(5*t^8*tf^2)/4+10*t^7*t0*tf^2-35*t^6*t0^2*tf^2+70*t^5*t0^3*tf^2-175/2*t^4*t0^4*tf^2+70*t^3*t0^5*tf^2-35*t^2*t0^6*tf^2+10*t*t0^7*tf^2-(5*t0^8*tf^2)/4)*x5;
 
 %% get coef4t %%%%%%%%
 coef4t=-(1/((t0-tf)^10))*5*(-(t^10/2)+(20*t^9*t0)/9-(15*t^8*t0^2)/4+(20*t^7*t0^3)/7-(5*t^6*t0^4)/6+t0^10/252+(25*t^9*tf)/9-25/2*t^8*t0*tf+150/7*t^7*t0^2*tf-50/3*t^6*t0^3*tf+5*t^5*t0^4*tf-(5*t0^9*tf)/126-(25*t^8*tf^2)/4+200/7*t^7*t0*tf^2-50*t^6*t0^2*tf^2+40*t^5*t0^3*tf^2-25/2*t^4*t0^4*tf^2+(5*t0^8*tf^2)/28+(50*t^7*tf^3)/7-100/3*t^6*t0*tf^3+60*t^5*t0^2*tf^3-50*t^4*t0^3*tf^3+50/3*t^3*t0^4*tf^3-(10*t0^7*tf^3)/21-(25*t^6*tf^4)/6+20*t^5*t0*tf^4-75/2*t^4*t0^2*tf^4+100/3*t^3*t0^3*tf^4-25/2*t^2*t0^4*tf^4+(5*t0^6*tf^4)/6+t^5*tf^5-5*t^4*t0*tf^5+10*t^3*t0^2*tf^5-10*t^2*t0^3*tf^5+5*t*t0^4*tf^5-t0^5*tf^5)*x0-(1/((t0-tf)^10))*5*((5*t^10)/2-(40*t^9*t0)/3+(115*t^8*t0^2)/4-(220*t^7*t0^3)/7+(35*t^6*t0^4)/2-4*t^5*t0^5+t0^10/84-(35*t^9*tf)/3+125/2*t^8*t0*tf-950/7*t^7*t0^2*tf+150*t^6*t0^3*tf-85*t^5*t0^4*tf+20*t^4*t0^5*tf-(5*t0^9*tf)/42+(85*t^8*tf^2)/4-800/7*t^7*t0*tf^2+250*t^6*t0^2*tf^2-280*t^5*t0^3*tf^2+325/2*t^4*t0^4*tf^2-40*t^3*t0^5*tf^2+(15*t0^8*tf^2)/28-(130*t^7*tf^3)/7+100*t^6*t0*tf^3-220*t^5*t0^2*tf^3+250*t^4*t0^3*tf^3-150*t^3*t0^4*tf^3+40*t^2*t0^5*tf^3-(10*t0^7*tf^3)/7+(15*t^6*tf^4)/2-40*t^5*t0*tf^4+175/2*t^4*t0^2*tf^4-100*t^3*t0^3*tf^4+125/2*t^2*t0^4*tf^4-20*t*t0^5*tf^4+(5*t0^6*tf^4)/2-t^5*tf^5+5*t^4*t0*tf^5-10*t^3*t0^2*tf^5+10*t^2*t0^3*tf^5-5*t*t0^4*tf^5+t0^5*tf^5)*x1-(1/((t0-tf)^10))*5*(-5*t^10+(280*t^9*t0)/9-(325*t^8*t0^2)/4+(800*t^7*t0^3)/7-(275*t^6*t0^4)/3+40*t^5*t0^5-(15*t^4*t0^6)/2+(5*t0^10)/252+(170*t^9*tf)/9-235/2*t^8*t0*tf+2150/7*t^7*t0^2*tf-1300/3*t^6*t0^3*tf+350*t^5*t0^4*tf-155*t^4*t0^5*tf+30*t^3*t0^6*tf-(25*t0^9*tf)/126-(105*t^8*tf^2)/4+1140/7*t^7*t0*tf^2-425*t^6*t0^2*tf^2+600*t^5*t0^3*tf^2-975/2*t^4*t0^4*tf^2+220*t^3*t0^5*tf^2-45*t^2*t0^6*tf^2+(25*t0^8*tf^2)/28+(110*t^7*tf^3)/7-290/3*t^6*t0*tf^3+250*t^5*t0^2*tf^3-350*t^4*t0^3*tf^3+850/3*t^3*t0^4*tf^3-130*t^2*t0^5*tf^3+30*t*t0^6*tf^3-(50*t0^7*tf^3)/21-(10*t^6*tf^4)/3+20*t^5*t0*tf^4-50*t^4*t0^2*tf^4+200/3*t^3*t0^3*tf^4-50*t^2*t0^4*tf^4+20*t*t0^5*tf^4-(10*t0^6*tf^4)/3)*x2-(1/((t0-tf)^10))*5*(5*t^10-(320*t^9*t0)/9+(435*t^8*t0^2)/4-(1300*t^7*t0^3)/7+(575*t^6*t0^4)/3-120*t^5*t0^5+(85*t^4*t0^6)/2-(20*t^3*t0^7)/3+(5*t0^10)/252-(130*t^9*tf)/9+205/2*t^8*t0*tf-2190/7*t^7*t0^2*tf+1600/3*t^6*t0^3*tf-550*t^5*t0^4*tf+345*t^4*t0^5*tf-370/3*t^3*t0^6*tf+20*t^2*t0^7*tf-(25*t0^9*tf)/126+(55*t^8*tf^2)/4-680/7*t^7*t0*tf^2+295*t^6*t0^2*tf^2-500*t^5*t0^3*tf^2+1025/2*t^4*t0^4*tf^2-320*t^3*t0^5*tf^2+115*t^2*t0^6*tf^2-20*t*t0^7*tf^2+(25*t0^8*tf^2)/28-(30*t^7*tf^3)/7+30*t^6*t0*tf^3-90*t^5*t0^2*tf^3+150*t^4*t0^3*tf^3-150*t^3*t0^4*tf^3+90*t^2*t0^5*tf^3-30*t*t0^6*tf^3+(30*t0^7*tf^3)/7)*x3-(1/((t0-tf)^10))*5*(-((5*t^10)/2)+20*t^9*t0-70*t^8*t0^2+140*t^7*t0^3-175*t^6*t0^4+140*t^5*t0^5-70*t^4*t0^6+20*t^3*t0^7-(5*t^2*t0^8)/2+5*t^9*tf-40*t^8*t0*tf+140*t^7*t0^2*tf-280*t^6*t0^3*tf+350*t^5*t0^4*tf-280*t^4*t0^5*tf+140*t^3*t0^6*tf-40*t^2*t0^7*tf+5*t*t0^8*tf-(5*t^8*tf^2)/2+20*t^7*t0*tf^2-70*t^6*t0^2*tf^2+140*t^5*t0^3*tf^2-175*t^4*t0^4*tf^2+140*t^3*t0^5*tf^2-70*t^2*t0^6*tf^2+20*t*t0^7*tf^2-(5*t0^8*tf^2)/2)*x4-(1/((t0-tf)^10))*5*(t^10/2-(40*t^9*t0)/9+(35*t^8*t0^2)/2-40*t^7*t0^3+(175*t^6*t0^4)/3-56*t^5*t0^5+35*t^4*t0^6-(40*t^3*t0^7)/3+(5*t^2*t0^8)/2-t0^10/18-(5*t^9*tf)/9+5*t^8*t0*tf-20*t^7*t0^2*tf+140/3*t^6*t0^3*tf-70*t^5*t0^4*tf+70*t^4*t0^5*tf-140/3*t^3*t0^6*tf+20*t^2*t0^7*tf-5*t*t0^8*tf+(5*t0^9*tf)/9)*x5;
 %% get coef5t %%%%%%%%
 coef5t=-(1/((t0-tf)^10))*5*(t^10/10-(5*t^9*t0)/9+(5*t^8*t0^2)/4-(10*t^7*t0^3)/7+(5*t^6*t0^4)/6-(t^5*t0^5)/5+t0^10/1260-(4*t^9*tf)/9+5/2*t^8*t0*tf-40/7*t^7*t0^2*tf+20/3*t^6*t0^3*tf-4*t^5*t0^4*tf+t^4*t0^5*tf-(t0^9*tf)/126+(3*t^8*tf^2)/4-30/7*t^7*t0*tf^2+10*t^6*t0^2*tf^2-12*t^5*t0^3*tf^2+15/2*t^4*t0^4*tf^2-2*t^3*t0^5*tf^2+(t0^8*tf^2)/28-(4*t^7*tf^3)/7+10/3*t^6*t0*tf^3-8*t^5*t0^2*tf^3+10*t^4*t0^3*tf^3-20/3*t^3*t0^4*tf^3+2*t^2*t0^5*tf^3-(2*t0^7*tf^3)/21+(t^6*tf^4)/6-t^5*t0*tf^4+5/2*t^4*t0^2*tf^4-10/3*t^3*t0^3*tf^4+5/2*t^2*t0^4*tf^4-t*t0^5*tf^4+(t0^6*tf^4)/6)*x0-(1/((t0-tf)^10))*5*(-(t^10/2)+(29*t^9*t0)/9-(35*t^8*t0^2)/4+(90*t^7*t0^3)/7-(65*t^6*t0^4)/6+5*t^5*t0^5-t^4*t0^6+t0^10/252+(16*t^9*tf)/9-23/2*t^8*t0*tf+220/7*t^7*t0^2*tf-140/3*t^6*t0^3*tf+40*t^5*t0^4*tf-19*t^4*t0^5*tf+4*t^3*t0^6*tf-(5*t0^9*tf)/126-(9*t^8*tf^2)/4+102/7*t^7*t0*tf^2-40*t^6*t0^2*tf^2+60*t^5*t0^3*tf^2-105/2*t^4*t0^4*tf^2+26*t^3*t0^5*tf^2-6*t^2*t0^6*tf^2+(5*t0^8*tf^2)/28+(8*t^7*tf^3)/7-22/3*t^6*t0*tf^3+20*t^5*t0^2*tf^3-30*t^4*t0^3*tf^3+80/3*t^3*t0^4*tf^3-14*t^2*t0^5*tf^3+4*t*t0^6*tf^3-(10*t0^7*tf^3)/21-(t^6*tf^4)/6+t^5*t0*tf^4-5/2*t^4*t0^2*tf^4+10/3*t^3*t0^3*tf^4-5/2*t^2*t0^4*tf^4+t*t0^5*tf^4-(t0^6*tf^4)/6)*x1-(1/((t0-tf)^10))*5*(t^10-(22*t^9*t0)/3+(93*t^8*t0^2)/4-(290*t^7*t0^3)/7+45*t^6*t0^4-30*t^5*t0^5+(23*t^4*t0^6)/2-2*t^3*t0^7+t0^10/84-(8*t^9*tf)/3+39/2*t^8*t0*tf-432/7*t^7*t0^2*tf+110*t^6*t0^3*tf-120*t^5*t0^4*tf+81*t^4*t0^5*tf-32*t^3*t0^6*tf+6*t^2*t0^7*tf-(5*t0^9*tf)/42+(9*t^8*tf^2)/4-114/7*t^7*t0*tf^2+51*t^6*t0^2*tf^2-90*t^5*t0^3*tf^2+195/2*t^4*t0^4*tf^2-66*t^3*t0^5*tf^2+27*t^2*t0^6*tf^2-6*t*t0^7*tf^2+(15*t0^8*tf^2)/28-(4*t^7*tf^3)/7+4*t^6*t0*tf^3-12*t^5*t0^2*tf^3+20*t^4*t0^3*tf^3-20*t^3*t0^4*tf^3+12*t^2*t0^5*tf^3-4*t*t0^6*tf^3+(4*t0^7*tf^3)/7)*x2-(1/((t0-tf)^10))*5*(-t^10+(74*t^9*t0)/9-(119*t^8*t0^2)/4+62*t^7*t0^3-(245*t^6*t0^4)/3+70*t^5*t0^5-(77*t^4*t0^6)/2+(38*t^3*t0^7)/3-2*t^2*t0^8+t0^10/36+(16*t^9*tf)/9-29/2*t^8*t0*tf+52*t^7*t0^2*tf-322/3*t^6*t0^3*tf+140*t^5*t0^4*tf-119*t^4*t0^5*tf+196/3*t^3*t0^6*tf-22*t^2*t0^7*tf+4*t*t0^8*tf-(5*t0^9*tf)/18-(3*t^8*tf^2)/4+6*t^7*t0*tf^2-21*t^6*t0^2*tf^2+42*t^5*t0^3*tf^2-105/2*t^4*t0^4*tf^2+42*t^3*t0^5*tf^2-21*t^2*t0^6*tf^2+6*t*t0^7*tf^2-(3*t0^8*tf^2)/4)*x3-(1/((t0-tf)^10))*5*(t^10/2-(41*t^9*t0)/9+(37*t^8*t0^2)/2-44*t^7*t0^3+(203*t^6*t0^4)/3-70*t^5*t0^5+49*t^4*t0^6-(68*t^3*t0^7)/3+(13*t^2*t0^8)/2-t*t0^9+t0^10/18-(4*t^9*tf)/9+4*t^8*t0*tf-16*t^7*t0^2*tf+112/3*t^6*t0^3*tf-56*t^5*t0^4*tf+56*t^4*t0^5*tf-112/3*t^3*t0^6*tf+16*t^2*t0^7*tf-4*t*t0^8*tf+(4*t0^9*tf)/9)*x4-(5*(-(t^10/10)+t^9*t0-(9*t^8*t0^2)/2+12*t^7*t0^3-21*t^6*t0^4+(126*t^5*t0^5)/5-21*t^4*t0^6+12*t^3*t0^7-(9*t^2*t0^8)/2+t*t0^9-t0^10/10)*x5)/(t0-tf)^10;
end