Second Order ODE with Exponential Coefficients

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  • #1
thatboi
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Hi all,
I have another second order ODE that I need help with simplifying/solving:
##p''(x) - D\frac{e^{\gamma x}}{A-Ae^{\gamma x}}p'(x) - Fp(x) = 0##
where ##\gamma,A,F## can all be assumed to be nonzero real numbers and ##D## is a purely nonzero imaginary number.
Any help would be appreciated!
 

Answers and Replies

  • #2
pasmith
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Set [itex]t = e^{\gamma x}[/itex]. Then [tex]
\gamma^2(1-t)t^2 \frac{d^2p}{dt^2} + \left(\gamma^2(1-t)t - \frac{\gamma D}{A} t^2\right) \frac{dp}{dt} - F(1-t)p = 0.[/tex] This looks like it should be solvable by Frobenius' method.
 

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