Find the solution of the differential equation that satisfies the given initial condition.

Question

dp/dt=2 sqrt(pt), P(1)=5

my answer: P=(2/3t^(3/2)+(15sqrt(5)-10)/15)^2

how is it wrong?

Answer 1

dp/dt = 2√(pt)
dp/√p = 2√t dt
2√p = 4/3 t^(3/2) + c
p = (2/3 t^(3/2) + c)^2

Now plug in t=1 to find c.