Is there a general solution for the following ODE?
$\displaystyle \frac{d^2 y}{dx^2}+f_1(x)\frac{dy}{dx}=f_2(x)$
Thank you.
Yes, note that if you let $\displaystyle \displaystyle Y = \frac{dy}{dx}$, then the DE becomes
$\displaystyle \displaystyle \frac{dY}{dx} + f_1(x)\,Y = f_2(x)$
which is first-order linear. Solve for $\displaystyle \displaystyle Y$ using the integrating factor method, then use this solution to solve for $\displaystyle \displaystyle y$.