Chapter 2.4, Problem 13P

Consider the initial value problem $y\text{'}=y^{1/3},y\left(0\right)=0$ from Example $3$ in the text.

Is there a solution that passes through the point $\left(1,1\right)$? If so, find it.

Is there a solution that passes through the point $\left(2,1\right)$? If so, find it.

Consider all possible solutions of the given initial value problem. Determine the set of values that these solutions attain at $t=2$.

The solution of initial vale problem $y\text{'}=y^{1/3},y\left(0\right)=0$ from Example $3$ is;

$y=\chi \left(t\right)=\{\begin{array}{l}0,if0\le t<t_0\\ \pm {\left[\frac{2}{3}\left(t-t_0\right)\right]}^{3/2},ift\ge t_0\end{array}$