$(1)$ First order linear ODE.

$($a$)$ Find the general solution of the equation:

$u^{\text{'}}=-3u-1+x^2$

$($b$)$ Find the solution of the above equation that satisfies $u(0)=0.$

$($c$)$ For $x>0,$ find the general solution of the equation:

$x{u}^{\text{'}}=u+x+2$