An ODE problem

  • Thread starter Juggler123
  • Start date
  • #1
83
0

Main Question or Discussion Point

Hi all,

I have an ODE of the form

[itex]\frac{d^{3}\psi}{d\xi^{3}}-A\left(\psi+\xi\frac{d\psi}{d\xi}\right)=0,[/itex]

where [itex]\psi=C_{1}U(\xi)+C_{2}V(\xi).[/itex]

Is there any transformation or inventive manipulation I can use here to obtain an ODE for [itex]\sigma=U(\xi)+V(\xi)[/itex]? As this is the quantity I would like to solve for.

Thanks.
 

Answers and Replies

  • #2
798
34
Hi !
y''(x)-A(y(x)+x*y'(x))=0
Let t=A*x²/2
Then a first solution is easy to see :
U=exp(t)=exp(A*x²/2)
Let y(x)=f(x)*exp(A*x²/2) and z=x*sqrt(A/2)
leading to an ODE which a solution is erf(z)
V= erf(x*sqrt(A/2))*exp(A*x²/2)
 

Related Threads on An ODE problem

  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
5
Views
3K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
10
Views
3K
  • Last Post
Replies
6
Views
783
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
3
Views
2K
Top