Why "crazy"? It looks pretty close to "easy" to me. Once you have applied the product rule to you can divide through by and the equation is very simple. I presume you know what a "finite difference method" is.
You are given the following two-point boundary value problem:
-(d/dx)(y*(e^x))+2y*(e^x)=(2-x)*(e^x), y(0)=y(1)=0
Simplify the equation and show that if the finite difference method is applied to the above problem, the resulting difference equation is:
-[(2-h)yi-1]+[4(1+h^2)yi]-[(2+h)yi+1]=2h^2(2-xi)
Why "crazy"? It looks pretty close to "easy" to me. Once you have applied the product rule to you can divide through by and the equation is very simple. I presume you know what a "finite difference method" is.