The given function is a variable separable differential equation. Combine like terms, integrate, apply the appropriate limits, and express V in terms of t. This is done as follows:
dV/dt = -3(V)^1/2
dV/-3V^1/2 = dt
[tex] \int\limits^V_m { \frac{1}{03 \sqrt{V} } } \, dV = \int\limits^t_0 {} \, dt [/tex]
m here is the initial V which is 225. Then after integrating,
-2/3 (√V - √225) = t
-2/3 (√V - 15) = t
[tex]V= \sqrt{ \frac{-3}{2}t+15 } [/tex]
That is the expression for V at time t. I hope I was able to help. Have a good day.
