Is the family of functions $\displaystyle y=c_{1}x^{-1}+c_{2}x+c_{3}x\ln(x)+4x^{2}$ a solution of the differential equation $\displaystyle x^{3}\frac{d^{3}y}{dx^{3}}+2x^{2}\frac{d^{2}y}{dx^{2}}-x\frac{dy}{dx}+y = 12x^{2}$? Assume an appropriate interval $I$ of definition for the solution.

You have only one attempt for credit.