Posted by Mina on .
solve secondorder initial value problem
y"(x)= x e^2x
y'(0)= 0
y(0)= 0

Calculus 
drwls,
First you need to integrate y"(x). This looks like a situation where "integration by parts" can be used.
Let u(v) = x and dv = e^2x dx
du = dx v = (1/2)*e^2x
Integral of u dv = uv  integral of v du
= (x/2)e(2x) + Integral of(1/2)*e^2x dx
Finish that off and use the y'(0) = 0 condition to solve for the arbitary constant. Once you have dy/dx, integrate again and use the initial condition at y(0) for the y(x) solution.