Thread: 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!!!

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

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.

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

Maybe your just have to approximate the solution.

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

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.

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

I remember the lecturer said something about Laplace Transform, but I'm sure how I can relate that to this question.