### Home > CALC > Chapter Ch10 > Lesson 10.1.3 > Problem 10-23

10-23.

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

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 (0.2, 1.222).

Now repeat this process three more times.