Question

Solve the Initial Value Problem:

Let k and Po be positive constants. P(0)=Po

dP/dt = kP^2

Answer 1

That looks like a separable first-order differential equation rather than calc 2, but here goes:

(separate both variables)
P^-2 dP = k dt
(integrate both sides)
-1/P = kt + C
P = -1 / (kt + C)
Po = -1 / C
C = -1 / Po
P = -1 / (kt + -1/Po)