Solve the ODE

  • Thread starter Gengar
  • Start date
  • #1
13
0
Hiya. I have to solve this bad boy under the assumptions that f, f' and f'' tend to 0 as |x| tends to infinity:

1/2(f')^2 = f^3 + (c/2)f^2 + af + b

where a,b,c are constants. My thoughts are use Fourier Transforms to use the assumptions given, but not sure how to do them on these terms. Thanks!
 

Answers and Replies

  • #2
798
34
Hi !

This is a separable ODE which (in theory) can be solved by direct integration :
df / sqrt(2 f^3 + c f^2 + 2af + 2b) = dx
But the integral involves very complicated elliptic functions, so that it will be of no use in practice.
In particular cases, i.e. for some particular values of a, b, c, it might reduce to simpler functions.
 

Related Threads on Solve the ODE

  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
4
Views
696
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
10
Views
3K
Replies
5
Views
954
  • Last Post
Replies
3
Views
3K
Top