Chapter 1.4, Problem 16P

One solution to the initial-value problem

$\frac{dy}{dx}=\frac{2}{3}{\left(y-1\right)}^{1/2}$, $y\left(1\right)=1$

is $y\left(x\right)=1$.Determine another solution to the initial-value problem. Does this contradict the existence and uniqueness theorem (Theorem 1.3.2)? Explain.