Efficient Solutions for Solving First Order ODE with Constant A

[BobbyBear]

Hello,
does anyone have any ideas on how to solve this first order ode?

$$\frac{dz}{dx} = \frac{z(x^4z^2-A^2)}{x(A^2-x^2z^4)}$$

where A is a constant.

It's neither exact, nor homogeneous . . . nor any of the types I've been able to find for which there are techniques for solving :(

Thank you :P

 

[kosovtsov]

You can find an integrating factor for your ODE to make it exact. The general solution in implicit form to your ODE is

x^2+z^2+A^2/(xz)^2= C,

where C is a constant.

 

[arildno]

Furthermore, you can solve the implicit equation for z given by kosostov by means of a clever trick.