Question

use Euler's method with a step size of 0.4 to approximate the solution of the differential equation y'=2xy; y(1)=2, at x=3

Answer 1

Approximate solution is 541.

Explanation:

y' = 2xy, Δx = 0.4.

Make a table:

x y y' y' Δx + y

1 2 4 4*0.4 + 2 = 3.6 <---this is the new y value.

1.4 3.6 10.08 7.632

1.8 7.632 27.48 18.624

2.2 18.624 81.95 51.70

2.6 51.70 268.85 159.24

3 159.24 955.44 541.4