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Consider $y''+4y=0$. By plugging in $y=\sum_{n=0}^{\infty}a_nx^n$, we find two power series solutions:


Which of the following statements are true?


The first is $\cos(2x)$ and the second is $\sin(2x)$ and they have a Wronskian of them is $2$.


By direct computation $y_1(0)=0$ and $y_1'(0)=0$, so the Wronskian is zero regardless of $y_2(0)$ and $y_2'(0)$.


The radii of convergence for both solutions are $\rho=1$.


The Wronskian of them at $x=0$ is $1$ and they form a fundamental set.

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