The diagram below shows a slope field.

1. Explain why $\frac { d y } { d x }$ must be a function of both $x$ and $y$.

   Hint (a):

   Are the slopes in the diagram parallel anywhere?

2. Sketch a solution curve that passes through $(0, 3)$.

   Hint (b):

   Your curve should look like a bell-shaped curve with a maximum at $(0, 3)$ and a horizontal asymptote of $y = 0$.

3. The slope field is for the differential equation $\frac { d y } { d x } = - 2 x y$. Find the equation of your solution curve.

   Hint (c):

   Once you integrate you should have $a '+ C'$. Use the point $(0, 3)$ to solve for the value of $C$.