This is the final part of a question: c)Find the solution of the differential equation $$x\cdot y''+2(1+2x)y'+4(1+x)y=32\exp(2x)$$ for which y=2exp(2) and y'=0 at x=1.
Here is the rest of the question:
a)Show that the substitution v=xy transforms the differential equation $$x\cdot y''+2(1+2x)y'+4(1+x)y=32\exp(2x) $$ $$x≠0$$ into the differential equation $$v''+4v'+4v=32\exp(2x)$$
b)Given that $v=a\exp(2x)$, where $a$ is a constant, is a particular integral of this transformed equation, find $a$. $(a=2)$
I know how to do the first two part but don't know how to continue.