Find the general solution to the differential equatio y" + 4y = cos 2x (where y' = ) dx

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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Find the general solution to the differential equation
y" + 4y = cos 2x
= Cos
(where y' = )
dx
Transcribed Image Text:Find the general solution to the differential equation y" + 4y = cos 2x = Cos (where y' = ) dx
Expert Solution
Step 1

When the right-hand side of a higher-order linear differential equation contains a function of the independent variable or constant, it becomes nonhomogeneous. The general solution of a non-homogeneous equation is the sum of two solutions. One solution is the complementary function, which is the solution of the corresponding homogeneous part. Another solution is the particular solution. By the principle of superposition, two solutions are then added to raise the general solution. 

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