Given a linear homogeneous 2nd order ODE of the form $$y''(x)+p(x)y'(x)+q(x)=0$$ the general solution is of the form $$y(x)=c_{1}y_{1}(x)+c_{2}y_{1}(x)$$ where ##c_{1},c_{2}## are arbitrary constants and ##y_{1}(x), y_{2}(x)## are linearly independent(adsbygoogle = window.adsbygoogle || []).push({}); basis solutions.

How does one prove that the general solution is given by the above?

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# I General solution to linear homogeneous 2nd order ODEs

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