# A simple(!) ODE

1. Jan 11, 2010

### Altabeh

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

How can you solve an arrogant ODE of form $${\frac {\left( {\frac {d}{dt}}\rho \left( t \right) \right) ^{2}}{\rho \left( t \right) }}=-3$$??

3. The attempt at a solution

I don't have any idea... maybe you do!

Thanks
AB

2. Jan 11, 2010

### Staff: Mentor

From this you get $(\rho '(t))^2 = -3\rho(t)$ from which you get two equations

$$\rho '(t) = +\sqrt{-3\rho(t)}$$

and

$$\rho '(t) = -\sqrt{-3\rho(t)}$$

Both are separable.

3. Jan 11, 2010

### Altabeh

Sorry. I'm a little bit confused right now, but how would this separation help us to get $$\rho(t)$$?

AB

4. Jan 11, 2010

### Count Iblis

If you divide both sides by sqrt(rho), you get:

rho'/sqrt(rho) = +/-sqrt(3) i

You can write this as:

d rho/sqrt(rho) = +/-sqrt(3) i dt

You can now integrate both sides.

5. Jan 11, 2010

### zcd

a simple ODE with a complex answer :D