# Math Help - Second Order Linear ODE with y(x) missing.

1. ## Second Order Linear ODE with y(x) missing.

Is there a general solution for the following ODE?

$\frac{d^2 y}{dx^2}+f_1(x)\frac{dy}{dx}=f_2(x)$

Thank you.

2. Yes, note that if you let $\displaystyle Y = \frac{dy}{dx}$, then the DE becomes

$\displaystyle \frac{dY}{dx} + f_1(x)\,Y = f_2(x)$

which is first-order linear. Solve for $\displaystyle Y$ using the integrating factor method, then use this solution to solve for $\displaystyle y$.