Solve the differential equation: dy/dx = (3x^2) / (y+1) with initial conditions x = -1, y = 2

Question

I have:
∫y + 1 dy = ∫3x^2 dx

(y^2 / 2) + y = x^3 + C

(2^2 / 2) + (2) = (-1^3) + C?
4 = -1 + C
5 = c

(y^2 / 2) + y = x^3 + 5

Is this correct?

Answer 1

You should probably solve for y using the quadratic formula. It comes out

y = √(2x^3+11) - 1

Answer 2

But other than solving for y, is it correct?