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

• Mar 15th 2011, 07:12 PM
Ehsan
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.
• Mar 15th 2011, 07:18 PM
Prove It
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 $\displaystyle y$.