$1-$S$.$ Solve for the general and particular solution of the following:

$y^{\text{'}}=\frac{x^3}{y^2}$;$y(1)=2$

$y^{\text{'}}=xy$;$y(0)=5$

$y^{\text{'}}=(y^{2}1)$;$y(1)=0$

Find the position function $($particular solution$)$ of a moving particle with the given acceleration, initial position and initial velocity: $a(t)=20,v_0=10,x_0=5$

Find the general and particular solution of the $DE{y}^{\text{'}}=\sqrt[\phantom{2}]{9-x^2}$ when $y(D)=5$