Solving an Arrogant ODE: Can You Do It?

[Altabeh]

Homework Statement

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

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