# Differential equations questions

1. Dec 3, 2004

### Fritz

I was trying to solve a 1st order D.E. and couldn't solve this:

ln 1/[(y^2)-1] I know the answer is 1/2 ln[(y-1)/(y+1)], but could figure out how this is so.

Also, I don't understand what method you'd use to get from y = Ae^-4x + Be^-6x to d2y/dx2 +10 dy/dx +24y + 0. I can eliminate the arbitrary constants in simpler D.E.'s, but not this one! Can someone go through a logical method?

Also, ytan(dy/dx) = (4 + y^2) sec^2(x). How, in this case, would you go about separating the variables?

2. Dec 3, 2004

### arildno

"Also, I don't understand what method you'd use to get from y = Ae^-4x + Be^-6x to d2y/dx2 +10 dy/dx +24y = 0. I can eliminate the arbitrary constants in simpler D.E.'s, but not this one! Can someone go through a logical method?"
Eeh, the expression for y(x) is called the GENERAL solution for the DE.
It SHALL have two arbitrary constants in its expression.

3. Dec 3, 2004

### Integral

Staff Emeritus
Zero is a perfectly good constant.

I have been looking at the first part of this problem but really do not understand the problem. Please give a concise statement of the DE. You may want to investigate our LaTex equation engine.

As for the second part simply compute the first and second derivative of the given solution, does it satisfy the DE?

To completly specify A and B you also need 2 initial or boundry conditions. Since those are not specified we can not go any further with the solution.

Last edited: Dec 3, 2004
4. Apr 8, 2010

Find a linear DE that has x and cosh x as solutions.

thanks

5. Apr 8, 2010