Question

Use Euler's Method with three equal step sizes to estimate the value of y(0.3) for the differential equation y ' = y, with y(0) = 1.

Can someone please confirm for me that this answer is 1.331? I am quite certain, but missed a similar question previously, so am doubting my calculations.

Thank you in advance!

Answer 1

1.331

Explanation:

y(0) = 1

y(0.1) − y(0) = y'(0) (0.1 − 0)

y(0.1) − 1 = 1 (0.1 − 0)

y(0.1) = 1.1

y(0.2) − y(0.1) = y'(0.1) (0.2 − 0.1)

y(0.2) − 1.1 = 1.1 (0.1)

y(0.2) = 1.21

y(0.3) − y(0.2) = y'(0.2) (0.3 − 0.2)

y(0.3) − 1.21 = 1.21 (0.1)

y(0.3) = 1.331

Your answer is correct!