How Do You Solve an ODE Involving Changing Tank Volume and Concentration?

[irNewton]

I am trying to solve this ODE and am stuck on this step! It is a mass balance of a tank where the volume and concentration are changing by time

Fin*Co - Fout*C1 = d(C1*V)/dt
Fin*Co - Fout*C1 = d(C1)/dt * V + d(V)/dt * C1

where V = A*h (area and height, where area is constant and height is changing with time)

Fin*Co - Fout*C1 = d(C1)/dt * Ah + d(h)/dt * A * C1

I understand you need to take the laplace somewhere...don't know where though!
Any ideas on how I would go about simplifying this?

Thank you!

 

[HallsofIvy]

You appear to have two unknown functions, C1 and V, but only one differential equation.
You cannot solve a single equation for two unknowns.