Find the solution of the differential equation dp/dt = sqrt(p*t) that satisfies the initial condition p(1)=5. p(t) =

Sqrt of (1/P) = √t  dt

integrate both sides and use initial conditions2(5)^1/2 = 2/3(1)^3/2 + C
C = 2√5 −2/3
therfore 
P(t) = (2/6 t ^2/3+√5 −2/6)^2