We want to iterate over the x′s and the y′s. The Euler method tells us to choose the sequences defined by:

$$x_{n+1}=x_n+0.1,y_{n+1}=y_n+0.1\cdot (x_n-y_n^2)$$

The initial conditions are $x_1=1.3$ and $y_1=2.35$.

1. Create a new document, press , and select Add Calculator.
2. Press and select Actions > Define.
3. Define $u(n)$: Enter the initialization on the first line and the recursive expression on the second line.
4. Define $v(n)$: Similarly, input the initialization and recursive formula for $v(n)$.

   

To compute $y(2.2)$, recall that $u(10)=x_{10}=2.2$. Therefore, $v(10)=y_{10}\approx y(2.2)$.

1. Enter $u(10)$ to confirm $x_{10}=2.2$.
2. Enter $v(10)$. The result should be $v(10)=1.42$, giving: $$y(2.2)\approx 1.42$$