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For the following set of ODE's using Laplace Transform. dy₁ dt dy₂ dt -2y₁ + y₂ = 2 +y₁ + y₂ = 0 a) Solve Yı(s) and Y₂(s). Then determine Y₂(s). b) Solve for y(t) and yz(t) yı(0) and y:(0) are zero.

For the following set of ODE's using Laplace Transform. dy₁ dt dy₂ dt -2y₁ + y₂ = 2 +y₁ + y₂ = 0 a) Solve Yı(s) and Y₂(s). Then determine Y₂(s). b) Solve for y(t) and yz(t) yı(0) and y:(0) are zero.

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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Problem 2 For the following set of ODE's using Laplace Transform. dy₁ + 2y₁ + y₂ = 2 dt dy2 +y₁ + y₂ = 0 dt a) Solve Yı(s) and Y2(s). Then determine Y₂(s). b) Solve for yı(t) and y2(t) yı(0) and y2(0) are zero.
Transcribed Image Text:Problem 2 For the following set of ODE's using Laplace Transform. dy₁ + 2y₁ + y₂ = 2 dt dy2 +y₁ + y₂ = 0 dt a) Solve Yı(s) and Y2(s). Then determine Y₂(s). b) Solve for yı(t) and y2(t) yı(0) and y2(0) are zero.
For Problem 2, Laplace each differential equation separately which leads to two algebraic equations in terms of Y1 and Y2 as a function of S. Substitute one of the equations into another and you should be able to get: Y2=-2/(S(S^2+3S+1)) Y1 +2(S+1)/(S(S^2+3S+1)) now, laplace inverse each equation separately (you need to use partial fraction expansion to separate the terms to be able to laplace inverse).
Transcribed Image Text:For Problem 2, Laplace each differential equation separately which leads to two algebraic equations in terms of Y1 and Y2 as a function of S. Substitute one of the equations into another and you should be able to get: Y2=-2/(S(S^2+3S+1)) Y1 +2(S+1)/(S(S^2+3S+1)) now, laplace inverse each equation separately (you need to use partial fraction expansion to separate the terms to be able to laplace inverse).
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