A simple(!) ODE

[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

[Mark44]

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.

[Altabeh]

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.

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

AB

[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.

[zcd]

a simple ODE with a complex answer :D