Given the initial$-$value problem

$y^{\text{'}\text{'}}\frac{3}{x}{y}^{\text{'}}-\frac{8}{x^2}y=0,y(1)=4,y^{\text{'}}(1)=2$

$($a$)$ The differential equation has solutions of the form $y=x^r.$ Find two independent solutions $y_1,y_2$ of the equation. Use the Wronskian to justify your answer.

$($b$)$ Give the general solution of the differential equation.

$($c$)$ Find the solution that satisfies the initial conditions.