# Solve the following ODE .. #1

• Sep 30th 2010, 09:09 AM
Liverpool
Solve the following ODE .. #1
Hello

I stopped at this one :S

$\dfrac{dy}{dx}=x^2+y^2$

How to solve this one ?!!!

What I know:
Exact / Separable / Homogeneous
All of them are failed

am thinking about substituting $t=x^2+y^2$

But those squares make my life hard

If it is x+y it would be easy ..
• Sep 30th 2010, 09:35 AM
Ackbeet
• Sep 30th 2010, 10:39 AM
Liverpool
Oh my god !!
So the differential equations are the same as the integrals
Sometimes its impossible to solve it ??
• Sep 30th 2010, 10:52 AM
Ackbeet
Quote:

So the differential equations are the same as the integrals.
Not quite sure what you mean here. The solution to any differential equation is obtained essentially by integrating. In addition, you can usually (perhaps always?) convert a DE into an equivalent integral equation if you wish. Integral equations have technical advantages over differential equations, especially with regard to the space of functions you consider for solutions (no differentiability required!)

Quote:

Sometimes its impossible to solve it?
Sometimes an analytical solution is not known. That might not mean that it's impossible to solve, just that we don't know what the solution is. In those cases, we usually hand it off to a computer.
• Sep 30th 2010, 11:26 AM
Jester
If you let

$y = - \dfrac{u'}{u}$

$u'' + x^2 u = 0$