Consider the following initial value problem,

$\frac{dy}{dx}=\frac{\frac{3}{2}{x}^{2}2x1}{y-1}$

$y(0)=3$

$($a$)$ Find the particular solution in explicit form, i$.$e$.$ solve for $y.($Note: at first, you may find that there are more than one solution, but only one of them makes mathematical sense$).(5$ points$)$

$($b$)$ Determine the interval in which the solution is valid. $(3$ points$)$