Consider the initial value problem

dy

dx $=2$pjyj

y $(0)=0$ ; $1<$ x $<1$:

Show that for any nonnegative constant c the function y $($x$)$ de$$ned by

y $($x$)$

$0$ for x $<$ c

$($x c$)2$ for x c ;

is a solution to the initial value problem. Thus in any open interval I containing $0$

there are in$$nitely many solutions. Explain why this does not contradict Theorem

$1.$