(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!!!

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- Apr 13th 2007, 08:03 AMchemengerHard 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, 08:16 AMCaptainBlack
- Apr 13th 2007, 08:24 AMchemenger
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, 08:32 AMCaptainBlack
- Apr 13th 2007, 09:36 AMThePerfectHacker
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, 05:57 PMchemenger
- Apr 14th 2007, 12:56 AMCaptainBlack
- Apr 14th 2007, 01:13 AMchemenger
I remember the lecturer said something about Laplace Transform, but I'm sure how I can relate that to this question.