Homework Help: Can I separate a differential equation?

1. May 16, 2013

sliken

Given the following differential equation

x*x''+(x')^2+y*y''+(y')^2=C

where C is a constant and all differentiation is with respect to time

Can i equal the first and second parts of the equation into different constants and solve separately?, meaning solving the system

x*x''+(x')^2=k^2
y*y''+(y')^2=C-k^2

2. May 16, 2013

Fightfish

No. Why would you expect that to hold true?
The equation can be slightly simplified though.
Think of how $x x'' + (x')^2$ can be rewritten.

3. May 16, 2013

Dustinsfl

You can write it has first order equations but I don't know if that is your aim.

4. May 17, 2013

vela

Staff Emeritus
[STRIKE]Yes. Why do you suppose you can do that?[/STRIKE] (Never mind.)

Last edited: May 17, 2013
5. May 17, 2013

LCKurtz

I don't see why the constant must be positive for the $x$ equation. But, more to the point, I am unconvinced that the answer is yes. It isn't like the eigenvalue situation you get in separation of variables in partial DE's because the two sides have different independent variables. Or maybe that isn't what your reasoning is.

6. May 17, 2013

Staff: Mentor

I like this idea.

7. May 17, 2013

vela

Staff Emeritus
Yeah, you're right. Never mind my earlier post.