Suppose the rate at which the volume in a tank decreases is proportional to the square root of the volume present. The tank initially contains 25 gallons, but has 20.25 gallons after 3 minutes. Solve for the general solution (do not solve for V).
The Attempt at a Solution
dV/dt = k√(V)
That's as far as I got. I know I have to "separate" the variables and whatnot, but there is no 't' to separate and differentiate from. I guess the equation would be: ∫1/√(V) dV = k∫ ___ dt
So my question is, since there is no 't' in the equation, what do I differentiate instead?