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1 / / / / 1^^ 1 / // | \₁ 1/ // ||^~ /////|55 // / //\ Euler's Method / / / / / AS |/ // // | \\ 17/11 AS ///// |/ // / || \ 1 / / / / / AS (f) List all equilibrium solutions in the direction field above, and sketch an approximate trajectory for the initial condition y(0) = 2.9. = 5) Use Euler's Method with step size h that is a solution to the initial value problem y' = 4y, |/ // // | \ 177777S 177777 a) Use Euler's Method with step size h = 1 to approximate values of y(2), y(3), y(4) for the function y(x) that is a solution to the initial value problem y = r²- y, y(1) = 3 2 classify the stability of each, 1/2 to approximate y(6) for the function y(x) y (3) 14 Use Euler's Method with step size h = 1 to approximate y(0) for the function y(t) that is a solution to the initial value problem y' = 2t - ty, Hint: Your initial condition is after the point you want to estimate to - you'll have to step backwards. y (2) = 2

1 / / / / 1^^ 1 / // | \₁ 1/ // ||^~ /////|55 // / //\ Euler's Method / / / / / AS |/ // // | \\ 17/11 AS ///// |/ // / || \ 1 / / / / / AS (f) List all equilibrium solutions in the direction field above, and sketch an approximate trajectory for the initial condition y(0) = 2.9. = 5) Use Euler's Method with step size h that is a solution to the initial value problem y' = 4y, |/ // // | \ 177777S 177777 a) Use Euler's Method with step size h = 1 to approximate values of y(2), y(3), y(4) for the function y(x) that is a solution to the initial value problem y = r²- y, y(1) = 3 2 classify the stability of each, 1/2 to approximate y(6) for the function y(x) y (3) 14 Use Euler's Method with step size h = 1 to approximate y(0) for the function y(t) that is a solution to the initial value problem y' = 2t - ty, Hint: Your initial condition is after the point you want to estimate to - you'll have to step backwards. y (2) = 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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Solve letter (b) Use Euler's method with step size h=1/2.

0 4 "1 Euler's Method 1 11/1 7 11 1 11111 / / //\ ////^ \ | / / / / / 11111 13 5 S > / / / / / ///// ///// 1/ / //\ \ 1. - y' = x² − y, 2 S \ / / / / / 17/11 1 (f) List all equilibrium solutions in the direction field above, and sketch an approximate trajectory for the initial condition y(0) = 2.9. y(3) = |/ // // | \\ /////|\~ (a) Use Euler's Method with step size h = 1 to approximate values of y(2), y(3), y(4) for the function y(x) that is a solution to the initial value problem y(1) = 3 (b) Use Euler's Method with step size h = 1/2 to approximate y(6) for the function y(x) that is a solution to the initial value problem y' = 4y, 1 4 ܐ ܐ ܐ ܐ | \ ܢ . |/ / / / / y (2) = 2 classify the stability of each, (c) Use Euler's Method with step size h = 1 to approximate y(0) for the function y(t) that is a solution to the initial value problem y' = 2t - ty, Hint: Your initial condition is after the point you want to estimate to - you'll have to step backwards.
Transcribed Image Text:0 4 "1 Euler's Method 1 11/1 7 11 1 11111 / / //\ ////^ \ | / / / / / 11111 13 5 S > / / / / / ///// ///// 1/ / //\ \ 1. - y' = x² − y, 2 S \ / / / / / 17/11 1 (f) List all equilibrium solutions in the direction field above, and sketch an approximate trajectory for the initial condition y(0) = 2.9. y(3) = |/ // // | \\ /////|\~ (a) Use Euler's Method with step size h = 1 to approximate values of y(2), y(3), y(4) for the function y(x) that is a solution to the initial value problem y(1) = 3 (b) Use Euler's Method with step size h = 1/2 to approximate y(6) for the function y(x) that is a solution to the initial value problem y' = 4y, 1 4 ܐ ܐ ܐ ܐ | \ ܢ . |/ / / / / y (2) = 2 classify the stability of each, (c) Use Euler's Method with step size h = 1 to approximate y(0) for the function y(t) that is a solution to the initial value problem y' = 2t - ty, Hint: Your initial condition is after the point you want to estimate to - you'll have to step backwards.
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