# Need help with differential equation of type y''+ay'+by=g(x)

1. Apr 21, 2010

### swebonny

1. The problem statement, all variables and given/known data

Is it possible to give a a value so that e^(-ax^2) becomes a solution to the differential equation y''(x)+x*y'(x)+y = 0

2. Relevant equations

3. The attempt at a solution

Hello!

I'm new to this forum and doesn't really know how the fancy Latex stuff works, but I hope you'll understand me. Anyhow, I have been sitting with this problem for a while.
Should I take the derivative of e^(-ax^2) and put it into the equation and in that way (somehow) find out x and a?

After the I have taken the derivative and put it into the equation I get this, which I'm fairly sure is correct :/

4a^2*(e^(ax^2))+2a(e^(ax^2))+2a(e^(ax^2))*x+(e^(ax ^2))= 0

What am I supposed to do next?

I hope you understand me.

Thanks. (nice forum btw)

2. Apr 21, 2010

### rock.freak667

e-ax2 ≥ 0 for all x, so you can divide throughout by it.

3. Apr 21, 2010

### Char. Limit

If such a condition were true, then you could not divide throughout by it. However, eax2 > 0 for all x, not ≥ 0 for all x.

So you can divide by eax2, but I wanted to correct that.