Question

Ice is forming in a pond at a rate given by dy/dx=ksqrt(t), where y is the thickness of the ice in cm at time t measured in hours since the ice started forming, and k is a positive constant. Find y as a function of t.

Answer 1

dy/dx=ksqrt(t)
dy=ksqrt(t)dt
Integrate both sides:
y=k(2/3)t^(3/2) + C
where C is an integration constant determined from initial conditions.

Thus
y = (2k/3)t^(3/2) + C