Solve ∫ (from 0 to t) of y(u)/sqrt{t-u}du=sqrt{t}

$$\int _ { 0 } ^ { t } \frac { y ( u ) } { \sqrt { t - u } } d u = \sqrt { t }$$

Solve for t

$$\left\{\begin{matrix}t=0\text{, }&u<0\\t=\frac{3}{4y}\text{, }&\left(u=0\text{ and }y>0\right)\text{ or }\left(y<\frac{3}{4u}\text{ and }u<\frac{3}{4y}\text{ and }u>0\text{ and }y>0\right)\end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}y=\frac{\sqrt{\frac{t-u}{t}}}{u}\text{, }&u\neq 0\text{ and }t>0\text{ and }t>u\\y\in \mathrm{R}\text{, }&t=0\text{ and }u<0\end{matrix}\right.$$