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.

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- Mar 15th 2011, 06:12 PMEhsanSecond Order Linear ODE with y(x) missing.
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. - Mar 15th 2011, 06:18 PMProve It
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 $\displaystyle \displaystyle y$.