kill(all)$

see:intergralequationfredholmfinalversion11outptheory.png (website)
peter.vlasschaert@gmail.com,31/12/2017

p1:y[0] =1;
p2:y[1]+1/2/6*(y[0]+4*exp(1/4)*y[1]+exp(0.5)*y[2])=exp(1/2);
p3:y[2]+1/6*(y[0]+4*exp(1/2)*y[1]+exp(1)*y[2])=exp(1);

p4:float(solve([p1,p2,p3], [y[0],y[1],y[2]]))[1];

I find on the internet ,books : wrong  : Y[2],for the same problem

p5:p4[1];
p6:p4[2];
p7:p4[3];

approximation :y(x)

p8:y(x)+1/6*(x*exp(0*x)*y[0]+4*x*exp(0.5*x)*y[1]+x*exp(1*x)*y[2]) =exp(x);

p9:solve(p8,y(x))[1];

p10:ev(p9,p5,p6,p7);

see : truebasic program to solve numerical. ( see :website :special topics)