# Homework Help: General Solution / Differential Equation

1. Feb 17, 2014

### emergentecon

1. The problem statement, all variables and given/known data
Find the general solution x(t) to the following differential equation:

dx/dt = 2t/5x

2. Relevant equations

dx/dt = 2t/5x

3. The attempt at a solution
My solution is:

∫5xdx = ∫2tdt
(5/2)x^2 = t^2 + C
x^2 = (2/5)(t^2 + C)
x = +-√[(2/5)(t^2 + C)]

However, when I put the problem in Mathematica, I get:

x = +-√(2/5)√(x^2 + 5C)

I don't see why it gets 5C as opposed to simply C?

Last edited: Feb 17, 2014
2. Feb 17, 2014

### Dick

No reason. C is an arbitrary constant and 5C is also an arbitrary constant. There's really no difference. Both are correct.

3. Feb 17, 2014

### emergentecon

I understood it to mean 5 * C . . . is that not correct?

4. Feb 17, 2014

### pasmith

Five times an arbitrary constant is an arbitrary constant.

5. Feb 17, 2014

### SteamKing

Staff Emeritus
Substitute your solution into the original ODE and see if it satisfies that equation. Do likewise with Mathematica's result.

6. Feb 17, 2014

### emergentecon

Hehe, fair enough.

Thanks!