We have the following Differential Equation with the initial condition
$$ \frac{dy}{dt}=\frac{1}{(y+1)(y-2)},~~ y(0)=0$$
By seperating the variables i got the general solution as follows
$$ \frac{1}{3}y^3-\frac{1}{2}y^2-2y=t+C_1 \implies 2y^3-3y^2 -12y=6t+6C_1$$
(1) What is a domain of definition?
(2) And what would be the domain of definition for the solution?