Differential equation help

1. Oct 6, 2008

youngoldman

d²y/ dx² = - h y / j

where h, j are constants. What's y?

2. Oct 6, 2008

youngoldman

This on its own is not actually a question in my assignment but it is a starting point I need to get the problem done.

3. Oct 6, 2008

gabbagabbahey

Can you think of a function whose second derivative is proportional to it?

4. Oct 6, 2008

youngoldman

I know y is an exponential function with a multiplication constant out the front, just not sure what the argument of the exponential is.

5. Oct 6, 2008

youngoldman

Actually I know it's going to be the sum of two exponentials with different multipliation contants and one will have the negative argument of the other.

6. Oct 6, 2008

youngoldman

In other words I know it's in the form

y = Aexp(c) + B exp (-c), just not sure what the c is.

7. Oct 6, 2008

gabbagabbahey

Since, the derivative is respect to x, why not try $kx$ where $k$ is a constant (it may be complex) for your argument? In fact, the general solution has two terms $y(x)=Ae^{kx}+Be^{-kx}$. When you plug this into your DE, what do you get?

8. Oct 6, 2008

youngoldman

and k = sqrt (- h/j)?

so it is a complex argument as I was expecting because a complex exp can be written in terms of sines and cosines, whose 2nd derivative is their own negative.

9. Oct 6, 2008

gabbagabbahey

Yes, exactly so you may as well write $y(x)=Csin(\frac{h}{j}x)+Dcos(\frac{h}{j}x)$

10. Oct 6, 2008

youngoldman

Thank you, gabbagabbahey.

11. Oct 6, 2008

klondike

This is a ay''+by'+cy=0 problem which has been discussed to death on every DE book. One should be able to write down the results (when b^2-4ac>0,<0 and = 0) while sleeping.