Question: the result requested can be obtained either by solving the...

The result requested can be obtained either by solving the given equations analytically or by plotting numerically generated approximations to the solutions. Try to form an opinion about the advantages and disadvantages of each approach. (A computer algebra system is recommended.)

Solve the initial value problem.

y' =

3x2

3y2 − 7

,    y(1) = 0

y3−7y=x3+−1

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. (Enter your answer using interval notation. Round your answer to three decimal places.)