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Differential Equations

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Moderate

Equation with Non-constant Coefficients

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

A

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

B

$x=0$ is a singular point.

C

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

D

This is a nonlinear equation.