Question $1.$

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

$\frac{dy}{dt}=2y+4-t$

$($b$)$ Find the value$($s$)$ of $b$ for which the given equation is exact:

$(x{y}^2+b{x}^{2}y)+(x+y)x^2\frac{dy}{dx}=0$

and solve it$.$