# First order DE separable

1. Sep 20, 2009

### dragonblood

I have tried to solve the differential equation

$$y'=x\sqrt{y}$$

like this:

$$y^{-\frac{1}{2}}y'=x$$
$$\int{y^{-\frac{1}{2}}}dy=\int{xdx}$$
$$y^{\frac{1}{2}}=\frac{x^2 +C}{4}$$
$$y=\left(\frac{x^2+C}{4}\right)^2$$

Is this the right way to solve it? Because the answer in my textbook says that the answer is
$$y=\pm\sqrt{x^2+C}$$

But I really can't see where I've gone wrong.

2. Sep 20, 2009

### arildno

The textbook's answer solves the diff.eq y'=x/y, rather than the one given.

See if your book may have mixed up the ordering of solutions to various diff.eq problems!

(Your own solution is correct for the problem given)

3. Sep 20, 2009

### CFDFEAGURU

Yes, I got the same solution as you did, dragonblood.

Wow, never thought I could discuss ODEs with someone named dragonblood.

Cool lol

Matt

4. Sep 20, 2009

### arildno

You wouldn't want to know what arildno means in Norwegian, SMLSKDMGLGURU!