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4. Rewrite the given differential equation as a system of first order differential d²y dt² equations: -2 + 2y = e²t Sint, 0

4. Rewrite the given differential equation as a system of first order differential d²y dt² equations: -2 + 2y = e²t Sint, 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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4. Rewrite the given differential equation as a system of first order differential equations: - 2+2y=e²t Sint, 0 < t <1, y(0) = -0.4 and y'(0) = -0.6 d²y dt² 5. Given: d²y dy 2 + 2y = e²t Sin t, 0<t<1, y(0) = -0.4 and y'(0) = -0.6, dt² dt dt Find by Euler's Method: (a) y(0.3) (b) d (0.3) dt Use a step size of h = 0.1 d²y dt² dy 6. Given: +2+y=et, y(0) = 1 and (0) = 2, Find by Euler's method: dt (a) y(0.8) (b) d (0.8) dt Use a step size of h = 0.2.
Transcribed Image Text:4. Rewrite the given differential equation as a system of first order differential equations: - 2+2y=e²t Sint, 0 < t <1, y(0) = -0.4 and y'(0) = -0.6 d²y dt² 5. Given: d²y dy 2 + 2y = e²t Sin t, 0<t<1, y(0) = -0.4 and y'(0) = -0.6, dt² dt dt Find by Euler's Method: (a) y(0.3) (b) d (0.3) dt Use a step size of h = 0.1 d²y dt² dy 6. Given: +2+y=et, y(0) = 1 and (0) = 2, Find by Euler's method: dt (a) y(0.8) (b) d (0.8) dt Use a step size of h = 0.2.
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Step 1: Given.

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Given: 4. d2ydt2-2dydt+2y=e2tsin(t), 0<t<1, y(0)=-0.4 and y'(0)=-0.6

To convert: The given second order differential equation to a system of first order differential equations.

 

 

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