Question $1$

$(20$ points$)$ Find the particular solution for $y(x)$ given $y(x_o=0)=5.$

$\frac{dy}{dx}=-2xy$

Recall: ${\displaystyle \underset{a}{\overset{b}{}}}\frac{1}{x}dx=lnx=ln(b)-ln(a).[Hint$: Use Separable ODE approach.$]$