Repeat Problem 13 using the initial-value problem y' = x -2y, y(0) = 1. The analytic solution is Problem 13 Consider the initial-value problem y' = 2y, y(0) = 1. The analytic solution is y = e2x. (a) Approximate y(0. 1) using one step and Euler's method. (b) Find a bound for the local truncation error in y1. (c) Compare the actual error in y1 with your error bound. (d) Approximate y(0.1) using two steps and Euler's method. (e) Verify that the global truncation error for Euler's method is O(h) by comparing the errors in parts (a) and (d).

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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.