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1. Find the explicit solution of the DE above.

1. Find the explicit solution of the DE above.

Advanced Engineering Mathematics
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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(a) (b) Consider the first order differential equations (DEs): = e, y(0) = 0. = 2(cosa)y, y(0) = 1. For part (a), do the following. 1. Find the explicit solution of the DE above. 2. Use Euler's method to compute an approximate solution for the DE on the interval [0,5]. Use a grid size of h = 0.1 and h =0.01. 3. Plot both the exact solution and the numerical solutions (for both values of h) on the same figure. 4. Compute the absolute and relative error at xz = 5 for both values of h. Repeat 1.-4. for part (b). Hand in a physical copy of your results, i.e. hand in your derivation of 1., the plots in 3., and the computed errors in 4. You may use the sample code provided on Moodle to do your computations.
Transcribed Image Text:(a) (b) Consider the first order differential equations (DEs): = e, y(0) = 0. = 2(cosa)y, y(0) = 1. For part (a), do the following. 1. Find the explicit solution of the DE above. 2. Use Euler's method to compute an approximate solution for the DE on the interval [0,5]. Use a grid size of h = 0.1 and h =0.01. 3. Plot both the exact solution and the numerical solutions (for both values of h) on the same figure. 4. Compute the absolute and relative error at xz = 5 for both values of h. Repeat 1.-4. for part (b). Hand in a physical copy of your results, i.e. hand in your derivation of 1., the plots in 3., and the computed errors in 4. You may use the sample code provided on Moodle to do your computations.
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