Consider the following initial value problem

$2y^{\text{'}\text{'}}-3y^{\text{'}}y=0$

$y(0)=2$

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

$($a$)$ Find the particular solution. $(3$ points$)$

$($b$)$ Determine the maximum value of the solution. $($Hint: this is from calculus $1),(1$ point$)$

$($c$)$ Find the point where the solution is zero. $(1$ points$)$