Chapter 1, Problem 21RE

To determine

(a)

To plot: The Different members of the families $y={\varphi }_1\left(x\right)=x^2+c_1$ and $y={\varphi }_2\left(x\right)=-x^2+c_2$.

To determine

(b)

To verify: The functions $y={\varphi }_1\left(x\right)=x^2+c_1$ and $y={\varphi }_2\left(x\right)=-x^2+c_2$ are solutions of the nonlinear first order differential equation ${\left(y^{\prime }\right)}^2=4x^2$.

To determine

(c)

The piece wise function which is a solution of the nonlinear differential equation ${\left(y^{\prime }\right)}^2=4x^2$.