$($a$)$ The differential equation $y^{\text{'}\text{'}}\frac{3}{x}{y}^{\text{'}}-\frac{8}{x^2}y=0$ has two solutions of the form $y=x^r.$ Find two independent solutions $y_1,y_2$ of the equation and calculate their Wronskian.

$($b$)$ Consider the initial$-$value problem

$y^{\text{'}\text{'}}p(x)y^{\text{'}}q(x)y=0,y(1)=2,y^{\text{'}}(1)=4.$

The functions $u_1(x)=2x^3,u_2(x)=3x^4-x^3,u_3(x)=-x^4$ are solutions of the differential equation. Give the general solution of the equation and find the solution of the initial$-$value problem.

A I have placed my work and my answer on my answer sheet.

B I want to have points deducted from my test for not working this problem.