Let c > 0. Show that the function is a solution to the initial value problem on the...

Let c > 0. Show that the function is a solution to the initial value problem on the interval –c < x < c. Note that this solution becomes unbounded as x approaches Thus, the solution exists on the interval with, but not for larger . This illustrates that in Theorem 1 the existence interval can be quite small (if c is small) or quite large (if c is large). Notice also that there is no clue from the equation dy/dx = 2xy² itself, or from the initial value, that the solution will “blow up” at