Chapter 2.1, Problem 29P

In Problems $29$ through $36$, obtain the requested resultsby solving the given equations analytically or, if necessary, by graphing numerically generated approximations to the solutions.

Solve the initial value problem $y\text{'}=(1+3x^2)/(12y^2-12y),y\left(0\right)=2$ and determine the interval in which the solution is valid.

Hint: To find the interval of definition, look for points where the integral curve has a vertical tangent.