A Hard differential equation

1. Sep 28, 2007

anirudhreddy

A Hard differential equation!!!!

Solve:

dy/dx = (x^2) + y

2. Sep 28, 2007

genneth

The rules of this forum requires you to show some working, so that we know where to begin helping.

Can you solve the homogeneneous equation: dy/dy - y = 0 ?
Can you find a particular integral?

3. Sep 28, 2007

HallsofIvy

That is a first order linear differential equation with constant coefficients- actually, it's about the easiest you could come up with. genneth suggested solving the "homogeneous equation" first. That would work.

But for linear first order equations, there is a standard formula for the "integrating factor". You could also use that.

4. Sep 28, 2007

mjsd

relevant equation:
if $$\frac{dy(x)}{dx}+P(x)\,y(x) = Q(x)$$
then
$$y(x) = e^{-\int P(\eta)\,d\eta} \int Q(x)\;e^{\int P(\xi)\,d\xi}\,dx$$

if you understand this you probably understand how to do your problem

5. Sep 28, 2007

anirudhreddy

thx guys

so........

first i should write it in the form

dy/dx + (-1)y = (x^2)

is that right?

Last edited: Sep 28, 2007
6. Sep 28, 2007

mjsd

the next step into better understanding this is to prove the formula above...

7. Oct 18, 2007

sennyk

Proof hint

The way I always proved this was to make the differential equation exact first. Then the rest is algebra; ahem, calculus.

8. Oct 20, 2007

Jwink3101

dy/dx-y=x^2 is a good start

To make your integrating factor, you do Exp(integral(-1dx)) (i hope that makes sense). Work it from there and see where you get.