The differential equation has the general solution

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

The differential equation

\dfrac{dy}{dx}=\dfrac{x^{2}}{y+1}

has the general solution

y(x)=\sqrt{\dfrac{x^{3}}{3}+C}-1

, where

C

is a constant. If

y(0)=2

, which value of

C

satisfies the initial condition? (a)

C=4

(b)

C=9

(c)

C=3

(d)

C=5