For $(1)$ and $(2),$ are they exact? If so$,$ solve.

$(1)2t3(2y-2)y^{\text{'}}=0$

$(2)\frac{dy}{dx}=-\frac{axby}{bxcy}$ where $a,b,cbxcy$ are constants

$(3)($a$)$ Show it is not exact

$t^2{y}^{3}t(1y^2)y^{\text{'}}=0$

$($b$)$ Verify that the ODE in part $($a$)$ becomes exact if multiplied by integrating factor $(t,y)=(t{y}^3{)}^{-1}$ and solve.