In cullen-zill chapter 6 equation 23 it says that(adsbygoogle = window.adsbygoogle || []).push({});

[itex]y_{2}(x)=y_{1}(x)\int\frac{e^{-\int P(x)dx}}{y_{1}^{2}(x)}dx[/itex]

is a solution of

[itex]y''+P(x)y'+Q(x)y=0[/itex]

whenever [itex]y_{1}(x)[/itex] is a known solution

Where does this come from? I would like to be able to prove this or find a proof somewhere.

My first thought is that since the general solution solution is [itex]y_{h}=C_{1}y_{1}+C_{2}y_{2}[/itex] then

[itex]y_{2}=v(x)y_{1}[/itex] where v(x) is just a function of x.

Thought maybe I could substitute that into the general form of the DE, but it doesn't seem to help much

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# Homework Help: Obtaining particular solution of second order linear DE from first

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