### Home > APCALC > Chapter 9 > Lesson 9.1.3 > Problem9-39

9-39.

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

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

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 solve for $y$ if $y(-2) = 2$. Use your graphing calculator to graph this actual solution and compare to your solution graph from part (a).

Use separation of variables and the integrate.

$\int\frac{dy}{y}=\int 2xdx$