# Hard 1st order ODE Question

• Apr 13th 2007, 07:03 AM
chemenger
Hard 1st order ODE Question
(dy/dx)^2 - 4x(dy/dx) + 6y = 0

The dy/dx squared term is kind of nasty. I've tried with all the substitutes I could think of, none of them worked.

Any hints would be appreciated. Thanks!!!
• Apr 13th 2007, 07:16 AM
CaptainBlack
Quote:

Originally Posted by chemenger
(dy/dx)^2 - 4x(dy/dx) + 6y = 0

The dy/dx squared term is kind of nasty. I've tried with all the substitutes I could think of, none of them worked.

Any hints would be appreciated. Thanks!!!

Well:

dy/dx = 2x +/- sqrt(4 x^2 -6)

so with some assumptions about smoothness of dy/dx you should be able to
proceed.

RonL
• Apr 13th 2007, 07:24 AM
chemenger
First off, thanks for the quick reply:)

Shouldn't that be dy/dx = 2x +/- sqrt(4 x^2 -6y)
I think you were missing a y.
I've actually thought about using the quadratic eqn. But I wasn't sure how to deal with the stuff that's under the sqrt sign.
Could you make it a bit clear? Thanks again.
• Apr 13th 2007, 07:32 AM
CaptainBlack
Quote:

Originally Posted by chemenger
First off, thanks for the quick reply:)

Shouldn't that be dy/dx = 2x +/- sqrt(4 x^2 -6y)
I think you were missing a y.

Yes it should, unfortunatly with the y there its not so simple:(

RonL
• Apr 13th 2007, 08:36 AM
ThePerfectHacker
Maybe your just have to approximate the solution.

Because it have the special form,
y'=f(x,y)
Apply Newton's Method.
• Apr 13th 2007, 04:57 PM
chemenger
Quote:

Originally Posted by ThePerfectHacker
Maybe your just have to approximate the solution.

Because it have the special form,
y'=f(x,y)
Apply Newton's Method.

I can't. The question says solve this ode, which means I'm gonna need an analytical solution.
• Apr 13th 2007, 11:56 PM
CaptainBlack
Quote:

Originally Posted by chemenger
I can't. The question says solve this ode, which means I'm gonna need an analytical solution.

How about a series solution? (looks a bit tricky though)

RonL
• Apr 14th 2007, 12:13 AM
chemenger
I remember the lecturer said something about Laplace Transform, but I'm sure how I can relate that to this question.