Exercise $3(15$ points$)$

Solve the given Cauchy$-$Euler equation $by$ variation $of$ parameters

$x^2{y}^{\text{'}\text{'}}-x{y}^{\text{'}}+y=2x$

Possible Answers

$(a.)y=C_{1}x+C_{2}xlnx+\frac{1}{2}{x}^3$

$(b.)y=C_{1}x+C_{2}xlnx+\frac{1}{2}x(lnx{)}^2$

$(c.)y=C_{1}x+C_{2}xlnx+x^3$

$(d.)y=C_{1}x+C_{2}xlnx+x(lnx{)}^2$

$(e.)$ None $of$ the above