# Tough Differential Equation (for me at least, and some others)

1. Apr 13, 2010

### Char. Limit

So, I tried putting this on the homework forum, but no one could think of a solution. So I'm going to put it here, hoping someone here would know...

How would you solve this?

$$\frac{dy}{dx}=5x^2-\frac{6}{y-2}$$

Note: This is no longer homework (it was a challenge question, but the challenge was thrown out; the teacher found it too difficult), so don't worry about spoiling anything.

Also: So far, (I'm learning diff EQs independently, and the challenge question was for a Calculus class) I only know the methods of substitution and finding an integration factor. I've heard of transforms, though. Could any of them help? Laplace, maybe?

2. Apr 13, 2010

### Mute

That's a non-linear differential equation. Methods like the Laplace transform or methods you learn in an ODE course won't be of much help.

Wolfram alpha doesn't even give a closed form solution:

http://www.wolframalpha.com/input/?i=solve+y%27%28x%29+%3D+5*x^2-6%2Fy%28x%29

(note that dy/dx = d(y-2)/dx, so you can make the substitution y - 2 = z, which I relabelled y)