Help with 1st order ode

  • Thread starter BobbyBear
  • Start date
  • #1
162
0
Hello,
does anyone have any ideas on how to solve this first order ode?

[tex]\frac{dz}{dx} = \frac{z(x^4z^2-A^2)}{x(A^2-x^2z^4)}[/tex]

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
 

Answers and Replies

  • #2
70
0
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.
 
  • #3
arildno
Science Advisor
Homework Helper
Gold Member
Dearly Missed
10,025
134
Furthermore, you can solve the implicit equation for z given by kosostov by means of a clever trick.
 

Related Threads on Help with 1st order ode

  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
5
Views
2K
Replies
4
Views
2K
  • Last Post
Replies
2
Views
2K
Replies
6
Views
4K
  • Last Post
Replies
2
Views
3K
Replies
2
Views
6K
Top