# Thread: Second order nonlinear nonhomogeneous differential equation

1. ## Second order nonlinear nonhomogeneous differential equation

Hello,

I am having a little trouble solving this equation:

$\displaystyle d^2y/dx^2 + A(dy/dx)^2*1/y + B/(y+C)^2 = D - Ex$

where A, B, C, D, and E are constants.

So far, I've found this

http://eqworld.ipmnet.ru/en/solutions/ode/ode0344.pdf

which would solve the first half of the equation. Is it possible to use a technique such as variation of parameters to solve the rest, or do I need a new approach entirely?

Many thanks in advance for any help on this!
OnePound

2. ## Re: Second order nonlinear nonhomogeneous differential equation

One may ask first - are the constants $\displaystyle A - E$ truely arbitrary constants?

3. ## Re: Second order nonlinear nonhomogeneous differential equation

Yes, I'm afraid they are!
The context is an equation modelling a rocket; A denotes a constant relating to the coefficient of friction, and E is the mass lost per second.

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