ZIIDAffEQModAp$126\mathrm{.}20$

Find two power series solutions of the given differential equation about the ordinary point $x=0.$

$y^{**}+4x{y}^{\text{'}}+4y=0$

$y_1=1-2x^2+2x^4-\frac{4}{3}{x}^6+$dots and $y_2=x-\frac{4}{3}{x}^3+\frac{16}{15}{x}^5-\frac{64}{105}{x}^7+$

$y_1=1-2x^2+2x^4-\frac{4}{3}{x}^6-$dots and $y_2=x+\frac{4}{3}{x}^3+\frac{16}{15}{x}^5+\frac{64}{105}{x}^7+$dots

$y_1=1+2x^2-2x^4+\frac{4}{3}{x}^6+$ and $y_2=x-\frac{4}{3}{x}^3+\frac{16}{15}{x}^5-\frac{64}{105}{x}^7+-$

$y_1=1-2x^2-2x^4-\frac{4}{3}{x}^6-$dots and $y_2=x-\frac{4}{3}{x}^3+\frac{16}{15}{x}^5-\frac{64}{105}{x}^7+$dots

$y_1=1-2x^2-2x^4-\frac{4}{3}{x}^6-$dots and $y_2=x+\frac{4}{3}{x}^3+\frac{16}{15}{x}^5+\frac{64}{105}{x}^7+$dots