Consider the ODE $y'=2\sqrt{|y|}$ where $y \in \mathbb{R}$ 
Show that there are many solutions to the ODE $y'=2\sqrt{|y|}$ with initial conditions $y(0)= 0$.

Later on in the question, it asks me to find all solutions with initial condition $y(0)=0$, so I don't think that's what I'm supposed to do here.  
Is showing $y(t) = 0$ and $y(t) = t^2$ both solve the ODE essentially answering the question?  Or are these really the same solution?
Any help would be greatly appreciated.
 A: The solutions of the differential equation $y'=2\sqrt{|y|}$ such that $y(0)=0$ are the functions $y_{a,b}$, indexed by $a$ and $b$ in $[0,+\infty]$, such that $$y_{a,b}(t)=\left\{\begin{array}{ccl}-(t+a)^2&\text{if}&t\lt-a\\0&\text{if}&-a\lt t\lt b\\(t-b)^2&\text{if}&t\gt b\end{array}\right.$$ In words, one starts from the graph of the function $y_{0,0}:t\mapsto\mathrm{sgn}(t)\cdot t^2$ and one translates the right part $t\geqslant0$ of the graph further to the right, at a finite or infinite distance $b$, and the left part $t\leqslant0$ of the graph further to the left, at a finite or infinite distance $a$. For example, $$y_{\infty,0}(t)=\left\{\begin{array}{ccl}0&\text{if}&t\leqslant0\\ t^2&\text{if}&t\gt 0\end{array}\right.$$
A: I think your examples answers the first question. If you have to show that there are many solutions, I think it is sufficient to show that there is more than one.
For the second question you'd have to show that those are really the only possible solutions - that there are no other solutions, so it is not sufficient just to show that your example satisfy the ODE.
