Find the general solution to the given equations.

$($a$)x{y}^{\text{'}}=y^{-3}$;

$($b$)y^{\text{'}}=\frac{x}{y^2\sqrt[\phantom{2}]{1+x}}$;

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

$($d$)y^{-1}dy+y{e}^{cosx}sinxdx=0$;

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