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

Multiple Choice

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

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