### Home > CALC > Chapter 10 > Lesson 10.1.3 > Problem10-23

10-23.

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

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

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

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

Now repeat this process three more times.