# Need help to solve one differential equation

by TimJ
Tags: differential, equation, solve
 P: 18 Does anybody know how to solve this differential equation: $$\frac{d^2 \theta}{dt^2}-A\sin(\theta)- \frac{B^2 \cos(\theta)}{ \sin^3(\theta) }=0$$ This is an equation that i get from the brachistochronic motion on the surface of a sphere.
HW Helper
Thanks
P: 26,167
Hi TimJ! Welcome to PF!

(have a theta: θ and an omega: ω )
 Quote by TimJ $$\frac{d^2 \theta}{dt^2}-A\sin(\theta)- \frac{B^2 \cos(\theta)}{ \sin^3(\theta) }=0$$
Try writing d2θ/dt2 = dω/dt = dω/dθ dθ/dt = ω dω/dθ = 1/2 d(ω2)dθ,

so d(ω2)/dθ = 2Asinθ + 2Bcotθcosec2θ
 P: 18 Thank you for your help.

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