Laplace Transforms · Superchallenge problem

Solve Abel's integral equation $\displaystyle\int_0^t \dfrac{y(\tau)}{\sqrt{t - \tau}}\,d\tau = t$ for $t \ge 0$ using the Laplace transform, and find $y(1)$. (You may use $\mathcal{L}\{t^{a}\} = \dfrac{\Gamma(a+1)}{s^{a+1}}$ and $\Gamma(\tfrac12) = \sqrt\pi$.)