What Is the General Solution of the Third-Order Homogeneous Cauchy $y=C_{1} x+C_{2} x \ln x+C_{3} x^{2} \ln x$

Multiple Choice

What is the general solution of the third-order homogeneous Cauchy Euler differential equation

A) $y=C_{1} x+C_{2} x \ln x+C_{3} x^{2} \ln x$
B) $y=C_{1} x+C_{2} x \ln x+C_{3} x(\ln x) ^{2}$
C) $y=C_{1} x^{-1}+C_{2} x^{-1} \ln \mathrm{x}+C_{3} x^{-1}(\ln x) ^{2}$
D) $y=C_{1} x^{-1}+C_{2} \ln \left(x^{-1}\right) +C_{3}\left(\ln \left(x^{-1}\right) \right) ^{2}$