Home > APCALC > Chapter 7 > Lesson 7.4.2 > Problem7-196

7-196.

If $(0, 4)$ is a point on the solution curve, use Euler’s Method to sketch the approximate solution curve for $0 ≤ x ≤ 2$ when $\frac { d y } { d x }= 2(x - y)$. Use $Δx = 0.5$.

Notice that you are given the derivative equation. That means you can calculate the slope at any given point.

$\text{For example, at (0, 4) the slope is }\frac{dy}{dx}=2(0-4)=-8.$

So if you were to draw a line segment starting at $(0, 4)$ with slope of $−8$, what would be the coordinate point at $x = 0.5$?

Use the coordinate point ($0.5$, ______) to calculate a new slope and find the coordinate point at $x = 1$.
Do the same to find the coordinate at $x = 1.5$.
And again at $x = 2$.

$(2, 1.5)$