Consider the differential equation $\frac{dy}{dx}=2xy.$

a$.$ Create the slope field for this diff'l eq'tn at the $9$ points indicated.

b$.$ Let $y=f(x)$ be the solution to the differential equation with the initial condition that $y=-1$ when $x=2.$ Use Euler's Method with three equal step sizes to approximate $f(2\mathrm{.}3).$

c$.$ Find the actual solution to this differential equation using the same initial condition.