# Differential equation problem

1. Dec 8, 2007

### tunabeast

1. The problem statement, all variables and given/known data
$$x^2\frac{dy}{dx}=\frac{2sqrt(y)}{x^4}$$

Where y(1)=3

2. Relevant equations

3. The attempt at a solution
$$\int \frac{dy}{2sqrt(y)}=\int \frac{dx}{x^4}$$

$$4sqrt(y)=\frac{-1}{3x^3}+c$$

$$c=4sqrt(3)+\frac{1}{3}$$

So i end up with

$$4sqrt(y)=\frac{-1}{3x^3}+4sqrt(3)+\frac{1}{3}$$

I'v gone wrong somewhere as the solution given does not match, i just can't spot where my mistake is. Thanks in advance for any help

2. Dec 8, 2007

### dotman

Hello,

How'd you get $$\int \frac{dy}{2\sqrt{y}}=\int \frac{dx}{x^4}$$
from

$$x^2\frac{dy}{dx}=\frac{2\sqrt{y}}{x^4}$$?

What happened to the $x^2$ term on the left?

3. Dec 8, 2007

### tunabeast

Sorry about that, stupid error. In the initial problem it should be $$\frac{2sqrt(y)}{x^2}$$

4. Dec 8, 2007

### Dick

Differentiate 4*sqrt(y). Do you get 1/(2*sqrt(y))?