# Second order nonlinear nonhomogeneous differential equation

• November 6th 2011, 10:40 AM
OnePound
Second order nonlinear nonhomogeneous differential equation
Hello,

I am having a little trouble solving this equation:

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

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
• November 6th 2011, 02:26 PM
Jester
Re: Second order nonlinear nonhomogeneous differential equation
One may ask first - are the constants $A - E$ truely arbitrary constants?
• November 7th 2011, 03:51 AM
OnePound
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.