Chapter 2.1, Problem 30P

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

Solve the initial value problem $y\text{'}=2x^2/(2y^2-6),y\left(1\right)=0$ 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.