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I have the following Bessel-like differential equation:

$$r^2T^{''}+K_1rT^{'}+(K_2r^2+K_3r^m)T=0$$

In this equation, $T=f(r)$ and $K_1$, $K_2$, $K_3$, and $m$ are parameters. I need an analytical solution for it. $T$ should be obtained as an explicit function of $r$. May somebody help me to find a solution?

Thanks in advance!

Ali Kefayati
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1 Answers1

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Some special cases:

$m=0,2$ : convertible to Bessel ODE

$m=1$ : convertible to degenerate hypergeometric ODE

$m=4$ : ODE of the form http://eqworld.ipmnet.ru/en/solutions/ode/ode0216.pdf

$m=-2$ : similar to Hunt for exact solutions of second order ordinary differential equations with varying coefficients. and can reduce to the doubly-confluent Heun equation

doraemonpaul
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