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Differential Equations

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Several Concepts for Second Order Linear Equations

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Consider the equation $2y''-y'-3=0$.

Which of the following statements are TRUE?

A

The characteristic equation for this differential equation is $2r^2-r-3=0$.

B

If $y_1, y_2$ are two solutions, then $y_1+y_2$ is also a solution.

C

If $y$ is a solution, then $y(x)+3x$ could be written as $C_1e^{x/2}+C_2$ for some $C_1, C_2\in\mathbb{R}$.

D

All of the above.