Given the differential equation y' ' + 4y' + 4y = 0, y(0) = − 1, y'(0) = == - 2 a) Apply the Laplace Transform and solve for Y(s) Y(s): = b) Now solve the IVP by using the inverse Laplace Transform y(t) = L¯¹{Y(s)} y(t) =

Given the differential equation y' ' + 4y' + 4y = 0, y(0) = − 1, y'(0) = == - 2 a) Apply the Laplace Transform and solve for Y(s) Y(s): = b) Now solve the IVP by using the inverse Laplace Transform y(t) = L¯¹{Y(s)} y(t) =

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 this differential equation and show your steps

Given the differential equation
y' ' + 4y' + 4y = 0, y(0) = − 1, y'(0) =
==
- 2
a) Apply the Laplace Transform and solve for Y(s)
Y(s):
=
b) Now solve the IVP by using the inverse Laplace Transform y(t) = L¯¹{Y(s)}
y(t) =

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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