The reduced equation for $x^2{y}^{\text{'}\text{'}}-3x{y}^{\text{'}}+3y=4x^3$ has solutions $of$ the form $y=x^r.$ The

general solution $of$ the given equation $is$:

$(a)y=C_{1}x+C_2{x}^3+\frac{1}{2}{x}^5$

$(b)y=C_1{x}^{-1}+C_2{x}^3-\frac{1}{3}{x}^4$

$(c)y=C_{1}x+C_2{x}^3+2x^{3}lnx-x^3$

$(d)y=C_{1}x+C_2{x}^{-3}+\frac{2}{3}{x}^4+x^{2}lnx$

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