: Consider the differential equation y" – 2y – 3y = 5 cos(2x). a) Verify that the family of functions y(x) = cje + cze³* 7 -cos(2x)- 13 4 -sin(2x) 13 is the general solution of the given DE. b) Find the solution to the given DE that satisfies the initial conditions y(0) = -4, y(0) = 4. %3D

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
: Consider the differential
equation
y" – 2y – 3y = 5 cos(2x).
a) Verify that the family of functions
4
-sin(2x)
13
7
y(x) = cje + cze³*
-cos(2x) –
13
is the general solution of the given DE.
b) Find the solution to the given DE that satisfies
the initial conditions y(0) = -4, y' (0) = 4.
Transcribed Image Text:: Consider the differential equation y" – 2y – 3y = 5 cos(2x). a) Verify that the family of functions 4 -sin(2x) 13 7 y(x) = cje + cze³* -cos(2x) – 13 is the general solution of the given DE. b) Find the solution to the given DE that satisfies the initial conditions y(0) = -4, y' (0) = 4.
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