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In Exercises 1 and 2, use Euler's method with the given step size At to approximate the solution to the given initial-value problem over the time interval specified. Complete the table below. Also, include a sketch of the graph of the approximate solution. You may do these problems directly on this sheet! dw 1. = (3 – w)(w + 1), w(0) = 0, 0

In Exercises 1 and 2, use Euler's method with the given step size At to approximate the solution to the given initial-value problem over the time interval specified. Complete the table below. Also, include a sketch of the graph of the approximate solution. You may do these problems directly on this sheet! dw 1. = (3 – w)(w + 1), w(0) = 0, 0

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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In Exercises 1 and 2, use Euler's method with the given step size At to approximate the solution to the given initial-value problem over the time interval specified. Complete the table below. Also, include a sketch of the graph of the approximate solution. You may do these problems directly on this sheet! dw 1. = (3 – w) (w + 1), w(0) = 0, 0<t< 5, At = 0.5 dt w(t) Wk f(tk, Wk) 3.5 1 2 3 2.5 4 6. 1.5 7 8 1 0.5 10 0.5 1.5 2 2.5 3 3.5 4 4.5 dy = e2/y. y(1) = 2, 1<t< 3, At = 0.5 y(t) 2. dt k f(tk, Yk) Yk 5 1 2 1 4 2 3 2 4 1 t 0.5 1 1.5 2.5 3
Transcribed Image Text:In Exercises 1 and 2, use Euler's method with the given step size At to approximate the solution to the given initial-value problem over the time interval specified. Complete the table below. Also, include a sketch of the graph of the approximate solution. You may do these problems directly on this sheet! dw 1. = (3 – w) (w + 1), w(0) = 0, 0<t< 5, At = 0.5 dt w(t) Wk f(tk, Wk) 3.5 1 2 3 2.5 4 6. 1.5 7 8 1 0.5 10 0.5 1.5 2 2.5 3 3.5 4 4.5 dy = e2/y. y(1) = 2, 1<t< 3, At = 0.5 y(t) 2. dt k f(tk, Yk) Yk 5 1 2 1 4 2 3 2 4 1 t 0.5 1 1.5 2.5 3
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