CPM Homework Help : CALC3RD Problem 10-33

Use Euler’s method with a step size of $h = 0.1$ to approximate $y(0.5)$ , where $y^\prime = x^2 + y^2$ and $y(0) = 1$ . Use the second derivative to determine whether this approximation is an underestimate or an overestimate.

Hint:

Since $h = 0.1$ , this is equivalent to $dx = 0.1$ .
Therefore $dy = 0.1(x^2 + y^2)$ .

Step 1:

Starting at $(0, 1)$ , $dy = 0.1$ , so the next point is $(0.1, 1.1)$ .

Step 2:

Starting at $(0.1, 1.1)$ , $dy = 0.122$ , so the next point is $(0.2, 1.222)$ .

Now repeat this process three more times.