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6. Consider the differential equation y' = y + 2x with y(0) = 1. (a) Find a closed form of the solution using the method of Taylor series about x = 0. (b) Use Euler's method to estimate y(0.6) with the following step sizes. (i) h = 0.3 (ii) h = 0.2

6. Consider the differential equation y' = y + 2x with y(0) = 1. (a) Find a closed form of the solution using the method of Taylor series about x = 0. (b) Use Euler's method to estimate y(0.6) with the following step sizes. (i) h = 0.3 (ii) h = 0.2

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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6. Consider the differential equation y' = y + 2x with y(0) = 1. (a) Find a closed form of the solution using the method of Taylor series about x = 0. (b) Use Euler's method to estimate y(0.6) with the following step sizes. (i) h = 0.3 (ii) h = 0.2
Transcribed Image Text:6. Consider the differential equation y' = y + 2x with y(0) = 1. (a) Find a closed form of the solution using the method of Taylor series about x = 0. (b) Use Euler's method to estimate y(0.6) with the following step sizes. (i) h = 0.3 (ii) h = 0.2
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