I have a problem in solving differential equation :
Let us consider following
$$ y' - \frac{2}{t}y = t^2e^t,\qquad y(1)=0.$$
First as I understood, using definition of Lipschitz condition, this equation has unique solution; second using Euler's method algorithm for approximation this equation has following form
set h=(b-a)/N;
t=a;
w=alpha;//( where alpha is initial value);
output(t,w);
for i=1,2.......N
w=w+h*f(t,w) (//f(t,y) is a function which we should find)
t=a+i*h;
output(t,w)
I know programming and can approximate it using program codes, but I want to solve it geometricaly or find unique solution, please help me.