$($a$)$ Solve the differential equation $y^{\text{'}}=\frac{1}{2}\sqrt[\phantom{2}]{1-16y^2}.$

$$

$)x^2+C(\frac{}{2}$

$($b$)$ Solve the initial$-$value problem $y^{\text{'}}=\frac{1}{2}x\sqrt[\phantom{2}]{1-16y^2},y(0)=0.$

$$

$)x(\sqrt[\phantom{2}]{\frac{}{2}}$