Answer the question 1. Given the following initial value problem over the interval from 0 to 1:dy= y+ 2.xe* , y(0) =1.dxа.Verify that the analytical solution is y=e*(x² +1).b.Implement Euler's method with step size h=0.25, and determine thetrue percent relative error at each step based on 1(a).С.Repeat part 1(b) with Heun's method. Compare the results. Whichmethod is the best? Explain with justification.

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Answered: 1. Given the following initial value…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.3: Euler's Method

Problem 22E

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1. Given the following initial value problem over the interval from 0 to 1: dy = y+2.xe* , y(0) = 1. dx а. Verify that the analytical solution is y= e*(x² +1). b. Implement Euler's method with step size h=0.25, and determine the true percent relative error at each step based on 1(a).