# [SOLVED] 1st Order Diff Equation

• Sep 22nd 2008, 01:20 PM
Ian1779
[SOLVED] 1st Order Diff Equation
Hi - I am just checking that I have got the right idea

The following first-order differential equation can be solved by separting the variables

$\displaystyle {\frac{dy}{dx}} = x^2 + 2x^2y^2(y>0)$

Am I right in saying that the following is the right separation so I can integrate and solve?

$\displaystyle \int {\frac{dy}{1+2y^2}}= \int x^2 dx$

Thanks in anticipation.
• Sep 22nd 2008, 01:21 PM
Moo
Hello,
Quote:

Originally Posted by Ian1779
Hi - I am just checking that I have got the right idea

The following first-order differential equation can be solved by separting the variables

$\displaystyle {\frac{dy}{dx}} = x^2 + 2x^2y^2(y>0)$

Am I right in saying that the following is the right separation so I can integrate and solve?

$\displaystyle \int {\frac{dy}{1+2y^2}}= \int x^2 dx$

Thanks in anticipation.

Yes you are right :)
• Sep 22nd 2008, 01:21 PM
icemanfan
Yes, that differential equation is separable and your setup is correct.
• Sep 22nd 2008, 01:22 PM
Matt Westwood
Looks okay to me.
• Sep 22nd 2008, 01:24 PM
Ian1779
Brilliant - thanks for the swift reply. It's really important I get this assignment right so trying to make sure it's all right (Happy)