Verify that $y_1(t)=1$ and $y_2(t)=t^{\frac{1}{2}}$ are solutions of the differential equation

$y^{\text{'}\text{'}}+(y^{\text{'}}{)}^2=0,$ for $t>0$

Then show that $y=c_1+c_2{t}^{\frac{1}{2}}$ is not, in general, a solution of this equation. Explain why this result does not contradict Theorem $3\mathrm{.}2\mathrm{.}2$ we learned in class.