(7) Consider the differential equation: y" + 4y = f(x) a) Find the solution to the homogeneous problem, f(x) = 0. b) Find the general solution when f(x) = COS x. c) Find the general solution when f(x) = cos 2x.
(7) Consider the differential equation: y" + 4y = f(x) a) Find the solution to the homogeneous problem, f(x) = 0. b) Find the general solution when f(x) = COS x. c) Find the general solution when f(x) = cos 2x.
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 (7): Consider the differential equation**
\[ y'' + 4y = f(x) \]
a) Find the solution to the homogeneous problem, \( f(x) = 0 \).
b) Find the general solution when \( f(x) = \cos x \).
c) Find the general solution when \( f(x) = \cos 2x \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2192a9f0-1ae9-4ed3-a35b-fc11f1172fc0%2Fe76fe9b4-aaa4-4eb2-ba0e-e5703ccb9177%2Ftd6guvl_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem (7): Consider the differential equation**
\[ y'' + 4y = f(x) \]
a) Find the solution to the homogeneous problem, \( f(x) = 0 \).
b) Find the general solution when \( f(x) = \cos x \).
c) Find the general solution when \( f(x) = \cos 2x \).
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