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Find the GS of y" + y = cos x + sinx

Find the GS of y" + y = cos x + sinx

Calculus: Early Transcendentals
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
**Find the General Solution (GS) of** \[ y'' + y = \cos x + \sin x \] This equation asks for the general solution to a second-order linear differential equation with constant coefficients. The equation is a non-homogeneous differential equation because of the presence of the functions \(\cos x\) and \(\sin x\) on the right-hand side. To solve this, you'll need to find the complementary solution (C.S.) related to the homogeneous equation \(y'' + y = 0\) and the particular solution (P.S.) for the non-homogeneous part. The general solution is the sum of these two solutions: \[ GS = C.S. + P.S. \]
Transcribed Image Text:**Find the General Solution (GS) of** \[ y'' + y = \cos x + \sin x \] This equation asks for the general solution to a second-order linear differential equation with constant coefficients. The equation is a non-homogeneous differential equation because of the presence of the functions \(\cos x\) and \(\sin x\) on the right-hand side. To solve this, you'll need to find the complementary solution (C.S.) related to the homogeneous equation \(y'' + y = 0\) and the particular solution (P.S.) for the non-homogeneous part. The general solution is the sum of these two solutions: \[ GS = C.S. + P.S. \]
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