TIFR-2012-Maths-D: 40

Question

True/False Question:

Consider the differential equations (with $y$ is a function of $x$)

1. $\begin{matrix} \frac{dy}{dx} & = & y\\ y\left ( 0 \right ) & = & 0 \end{matrix}$
2. $\begin{matrix} \frac{dy}{dx} & = & \left | y \right |^{\frac{1}{3}}\\ y\left ( 0 \right ) & = & 0. \end{matrix}$

Then $(1)$ has infinitely many solutions but $(2)$ has finite number of solutions.