Nonlinear Differential equation and simplification techniques

[arroy_0205]

Suppose there is a nonlinear differential equation in y(x) of the form:
<br /> y&#039;&#039;(x)(c_1+a^2y(x)^2)+p_1(x)y&#039;(x)^3-by(x)y&#039;(x)^2+p_2&#039;(x)(c_1+a^2y(x)^2)+hy(x)=0<br />
Where prime denotes derivative with respect to the argument x; p_i are known variables, and c,a,b,h are constants. Is there any way to write this equation in a more tractable form? It will be helpful for my purpose to express it in the form
<br /> y&#039;&#039;(x)+u(x)y(x)=My(x)<br />
Can anybody suggest an way? If it is not possible then can you suggest in general how far one can go with such complicated nonlinear equations analytically, instead of numerically?
In fact, I am not looking for an exact solution but looking at the behaviour of y(x).

 

[arroy_0205]

In my prevoius post I actually meant to rewrite the equation in the form
<br /> w&#039;&#039;(x)+u(x)w(x)=Mw(x)<br />
where w(x) is obtained by some transformaion on y(x).