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" + y = 12 cos 2x - sin x. A. " + y = sin 3x +4 cos x. A

" + y = 12 cos 2x - sin x. A. " + y = sin 3x +4 cos x. A

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 4E
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E D(D - 2)°y = 48e E (D - 18D2 + 81)y = 36e3*. %3D . (D² + 16)y = 14 cos 3x. (4D? + 1)y = 35 sin 3x. . y +16y = 24 sin 4x. D. y" + 16y = 48 cos 4x. 1. y"+ y = 12 cos 2x - sin x. 2 y" +y sin 3x + 4 cos x. 3. (D? - 2D + 5)y = e cos 2x. Hint: Use the exponential shift followed Dy formula (3) of Section 50. 1. (D² + 2D + 5)y = e* sin 2x. Ans. y = (c, + c2 x + x)e3* + (c3 +c,xe Ans. y = c1 cos 4x + c2 sin 4x + 2 cos 3x. Ans. y = c, cos x + c2 sin x- sin 3x. Ans. y (c,-3x) cos 4x + cz sin 4x. Ans. y = c cos 4x + (c, + 6x) sin 4x. Ans. y = (c, + x) cos x +c, sin x-4 cos 2x. Ans. y = c, cos x + (c, + 2x) sin x - sin 3x. %3D %3D %3D %3D %3D Ans. y = e(c, cos 2x + c, sin 2x) + xe* sin Zx. Ans. y = e*(c, cos 2x + c, sin 2x) - xe cos 2X.
Transcribed Image Text:E D(D - 2)°y = 48e E (D - 18D2 + 81)y = 36e3*. %3D . (D² + 16)y = 14 cos 3x. (4D? + 1)y = 35 sin 3x. . y +16y = 24 sin 4x. D. y" + 16y = 48 cos 4x. 1. y"+ y = 12 cos 2x - sin x. 2 y" +y sin 3x + 4 cos x. 3. (D? - 2D + 5)y = e cos 2x. Hint: Use the exponential shift followed Dy formula (3) of Section 50. 1. (D² + 2D + 5)y = e* sin 2x. Ans. y = (c, + c2 x + x)e3* + (c3 +c,xe Ans. y = c1 cos 4x + c2 sin 4x + 2 cos 3x. Ans. y = c, cos x + c2 sin x- sin 3x. Ans. y (c,-3x) cos 4x + cz sin 4x. Ans. y = c cos 4x + (c, + 6x) sin 4x. Ans. y = (c, + x) cos x +c, sin x-4 cos 2x. Ans. y = c, cos x + (c, + 2x) sin x - sin 3x. %3D %3D %3D %3D %3D Ans. y = e(c, cos 2x + c, sin 2x) + xe* sin Zx. Ans. y = e*(c, cos 2x + c, sin 2x) - xe cos 2X.
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