How Can I Solve This Complex Differential Equation?

[w00dy85]

Hi everone, i am trying to Solve the N.-St.-equation for a special problem - i was able to solve my equation for the 2 velocity components - the 3rd velocity component i seperetated - one term of the Seperation i was able to solve with a Bessel function, the 2nd term now looks like this:

h[z]'' - 2 α Tan(z) h[z]' + ((λ*2α)/c2 - 1/Cos[z]^2) h[z] = 0

h[z] = ?

 

[kosovtsov]

Maple solves your ODE via Legendre functoins.

 

[w00dy85]

thank you

i tried also to solve it with mathematica or wolfram alpha - i now get an solution, what is a little bit strange, because the last few days mathematica was not able to solve my equation, probably all my transformations of the equation were useful - i hope so, but i am afraid, that i made a small mistake somewhere !

I will controll my equation and the transformation steps tomorrow, then i will know if i posted the correct form of the formula here !

But still, in case the posted formula is correct, some more Information how to solve the equation would be useful