Chapter 9.1, Problem 8E

(a)

To determine

To describe: The graph of a solution of the equation $y^{\prime }=x{y}^3$ when x is close to $0$ and when x is large.

(b)

To determine

To verify: All members of the family $y={\left(C-x^2\right)}^{\frac{-1}{2}}$ are solutions of the differential equation $y^{\prime }=x{y}^3$.

(c)

To determine

To sketch: Several members of the family of solution of the function in the same plot.

(d)

To determine

To find: The solution of initial value problem $y^{\prime }=x{y}^3$ with initial condition $y\left(0\right)=2$.