Solve the system of first-order IVPS using Laplace Transform:x' = yx(0) = 2y' == -Xy(0) = –1Please type in your step-by-step solution. You may use the Laplace Transform Table and/or technology to find the Partial FractionDecomposition when appropriate. Consider the IVPy" + 2y =8(t – n) ; y(0) = 0, y'(0) = 0n=11. Describe the physical system that is being modeled by this differential equation. What does each component represent? What doyou expect the system to behave?2. Solve the IVP using Laplace Transform.3. Optional: Use technology to graph the solution. Does it match what your expectation? Please upload the graph here.

"Since you have asked multiple question, we will solve the first question for you. If you want any…

Solve the system of first-order IVPS using Laplace Transform: x' = y x(0) = 2 y' = - y(0) = –1 Please type in your step-by-step solution. You may use the Laplace Transform Table and/or technology to find the Partial Fraction Decomposition when appropriate.

Solve the system of first-order IVPS using Laplace Transform: x' = y x(0) = 2 y' = - y(0) = –1 Please type in your step-by-step solution. You may use the Laplace Transform Table and/or technology to find the Partial Fraction Decomposition when appropriate.

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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Question

Solve the system of first-order IVPS using Laplace Transform:
x' = y
x(0) = 2
y' =
= -X
y(0) = –1
Please type in your step-by-step solution. You may use the Laplace Transform Table and/or technology to find the Partial Fraction
Decomposition when appropriate.

Consider the IVP
y" + 2y =
8(t – n) ; y(0) = 0, y'(0) = 0
n=1
1. Describe the physical system that is being modeled by this differential equation. What does each component represent? What do
you expect the system to behave?
2. Solve the IVP using Laplace Transform.
3. Optional: Use technology to graph the solution. Does it match what your expectation? Please upload the graph here.

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