In one of my test it given to prove that $x^3$ and $x^2|x|$ are linear independent solutions of the differential equation $x^2y’’-4xy’+6y=0$ on $\mathbb R$( here $x$ is independent variable).
But according to me it’s Cauchy Euler equation having general solution as $y=c_1x^3+c_2x^2$, where $c_1$ and $c_2$ are arbitrary constants. How can be $x^2|x|$ a solution of given ODE as I am unable to find its by giving particular values of constants $c_1$ and $c_2$? Please help me to solve it . Thank you.