Use Euler's method with step size h = 0.2 to approximate the solution to the initial value problem y' = (y + 3), y(1) = 1 at the points a = 1.2, 1.4, 1.6, and 1.8. Compare these to the actual values y(1.2), y(1.4), y(1.6), and y(1.8). What do you notice about the difference between the approximated values versus the exact values as the x value increases?

Use Euler's method with step size h = 0.2 to approximate the solution to the initial value problem y' = (y + 3), y(1) = 1 at the points a = 1.2, 1.4, 1.6, and 1.8. Compare these to the actual values y(1.2), y(1.4), y(1.6), and y(1.8). What do you notice about the difference between the approximated values versus the exact values as the x value increases?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Use Euler's method with step size h = 0.2 to approximate the solution to the initial value problem
y' = (y + 3), y(1) = 1 at the points a = 1.2, 1.4, 1.6, and 1.8. Compare these to the actual
values y(1.2), y(1.4), y(1.6), and y(1.8). What do you notice about the difference between the
approximated values versus the exact values as the x value increases?

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