Easy# Series Solutions of a Second Order ODE

DIFFEQ-ENEZSE

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

$$y_1(x)=\sum_{k=0}^{\infty}\frac{(-4)^k}{(2k)!}x^{2k}$$

$$y_2(x)=\sum_{k=0}^{\infty}\frac{(-4)^k}{(2k+1)!}x^{2k+1}$$

Which of the following statements are true?