Draw a slope field for $\frac { d y } { d x } = 2 x y$ for $−2 ≤ x ≤ 2$.

1. If $y(−2) = 2$, use Euler's Method to draw a solution curve for $y$ using $∆x = 1$.

   Hint (a):

   If $dx = 1$, then $dy = 2xy$.
   The initial point is $(−2, 2)$.
   The next point is $(–2 + dx, 2 + dy)$.

2. Use implicit integration to find a solution, $y$, for the differential equation if $y(−2) = 2$. Use your graphing calculator to graph this actual solution and compare to your solution graph from part (a).

   Steps (b):

   Use separation of variables and the integrate.