Solve the Differential Equation: y'=(3x^2)/Sin(y) when y(0)=0

We have a variable-separable differential equation with an initial condition.

Rewrite y' to dy/dx to be able to separate the x and y variables.
Collect all like terms on each side by multiplying each side by sin(y) and dividing both sides by 3x^2.
Integrating both sides.
Solving for y.
Because we have an initial condition of y(0)=0, we can use this to solve for the constant C. Plug 0 in for x and y and solve for C. We find that C = 1
Rewriting our equation with 1 as the constant we get y=ArcCos[-x^3+1) as our final answer.