I'm not entirely too sure how to approach this question here on the topic of differential equations:
It is possible for an IVP to have multiple solutions. Consider the initial value problem
\begin{align} \frac{dy}{dx}=3y^{\frac{2}{3}} \ \ with \ \ y (0)=0 \end{align}
Show that the following function is a solution of this IVP.
\begin{cases} x^3 & for \ \ x < 0 \\ \\ 0 & for\ \ x \geq 0 \end{cases}
One solution is the zero function. The given function is also a solution since $\frac {dy} {dx}=3x^{2}=3y^{2/3}$ for $x<0$ and $\frac {dy} {dx}=3y^{2/3}=0$ for $x \geq 0$. Hence there are two different solutions to the IVP.