I was attempting to solve a differential equation using separation of variables' method. After some calculations I got to this:(adsbygoogle = window.adsbygoogle || []).push({});

$$ \frac 1 {a(r)} \frac k r \frac d {dr} \left(r \frac {da(r)}{dr} \right) = f $$

and I rearranged to this:

$$\frac k r \frac {da(r)}{dr} + \frac{d^2a(r)}{dr^2} = fa(r)$$

##k## and ##f## are constants. In a more elegant way:

$$ \ddot a + \frac k r \dot a - fa = 0 $$

Then I realized I don't know how to solve it because of ## \frac 1/r ##. I never studied how to solve differential equation with non-constant coefficients. Can anybody help me? Or suggest me some reading that can help me?

Thank you

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# I Non-constant coefficient

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