Hi, I have a problem and I am wondering if anyone can help... There is(adsbygoogle = window.adsbygoogle || []).push({});

this ODE, where P(x) and Q(x) are known functions:

y''(x)+P(x) y'(x)+Q(x) y(x)=0 (1)

This ODE cannot be solved analytically in general. However I can solve the following one (for the specific P(x) and Q(x) I have only):

f''(x)+P(x) f'(x)+Q(x)/x f(x)=0 (2)

The difference is in the third term :Q(x) => Q(x)/x. Does anyone know

of a transformation y(x)=>f(x) such that eq. (1) can be transformed

into eq. (2), which is solvable (as I said with the specific P & Q I

have, not in general)?

Cheers

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# Transforming an ODE

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