Find the Particular Solution of the Differential Equation $y^{\prime}-\frac{y}{x}=x^{2}$ If $y=4$ When $x=1$

Multiple Choice

Find the particular solution of the differential equation $y^{\prime}-\frac{y}{x}=x^{2}$ if $y=4$ when $x=1$ .

A) $y=\frac{1}{2} x^{3}+\frac{7}{2} x$
B) $y=\frac{1}{2} x^{2}+\frac{7}{2}$
C) $y=x^{3}+7 x$
D) $y=\frac{1}{2} x+\frac{7}{2 x}$