Upgrade subject to access all content

Consider the equation $x^2y''-6xy'+10y=0$. Which of the following statements are true?

The characteristic equation is $x^2r^2-6xr+10=0$.

$x=0$ is a singular point.

$x^2$ and $x^5$ are two solution but their Wronskian at $x=0$ is zero, so $x^2$ and $x^5$ are linearly dependent.

This is a nonlinear equation.