# Particular solution of a second order differential equation

I have a general (maybe naive) question. Let's suppose I have the following diff. eq.$$y''(x)+a~y'(x)=b(x)$$ To solve it, I cand do a change of variable and write: $$u'(x)+a~u(x)=b(x)$$ Then, if I find the particular solution to be $$u_p(x)=f(X)$$ Can I find the particular solution of the original equation just by doing: $y_p(x)=\int u_p(x) dx$ ?

Thank you.

• You have $u=y'$ and you need $y$. Therefore... – Siminore May 6 '15 at 14:57
• Yeah...Just to be sure. Thank you :) – lailola May 11 '15 at 14:21