let f be the function satisfying f'(x) = x√f(x) for all real numbers where f(3) = 25 find f'(3)

Answer 1

I get y = 1/12 (4x^3 + 12c x^(3/2) + 9c^2)
using y(3) = 25, that gives
y = 1/9 (x^3 -6(√3±5) x^(3/2) + 252±99√3)
Looks pretty hairy, so check my math