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Differential Equations

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Series Solutions of a First Order ODE

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Consider the equation $y'-2y=0$. Which of the following statements are true?

Select ALL that apply.

A

$y=a_0\sum_{n=0}^{\infty}\frac{2^nx^n}{n!}$ is a power series solution.

B

$y=a_0\sum_{n=0}^{\infty}\frac{(-2)^nx^n}{n!}$ is a power series solution.

C

The radius of convergence for any power series solution is infinity.

D

There exists one series solution such that the radius of convergence is finite.