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

  1. #1
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    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.
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  2. #2
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    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.
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