$(1$ point$)$

Solve $y^{\text{'}}+3x^{-1}y=x^2,y(1)=0.$

$(a)$ Identify the integrating factor, $(x).$

$(x)=$

$(b)$ Find the general solution.

$y(x)=$

Note: Use $C$ for $an$ arbitrary constant.

$(c)$ Solve the initial value problem $y(1)=0.$

$y(x)=$