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(4D2 - 1)y = e*/2 + 12e.

(4D2 - 1)y = e*/2 + 12e.

Advanced Engineering Mathematics
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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Hi, pls help me solve the highlighted item in the attached image below. Please show complete solution. Need it asap. Thank you.

 

Topic: Differential Equations

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(D2 + 36)y = sin 6x. . (D2 + 9)y = sin 3x. %3D %3D L (D2 + 36)y = cos 6x. 4x Ans. y = C1e** + Cz e* + 2e?z Ans. y = c,e* + Cze' Ans. y C1e**+ (c2 + 3xje* Ans. y = ce*+ (C2- 4x)e xe* + (c2 + x)e" %3D . (D² + 3D - 4)y = 12e2x. . (D² + 3D-4)y 21e3* (D? + 3D - 4)y (D? + 3D - 4)y 20e,4x. (D² - 3D + 2)y = e + e2x. (4D2 - 1)y = e/2 + 12e. E D(D – 2)y = 48e2. E (D - 18D2 + 81)y = 36e3*. + te. %3D -4x 15e. 1 Ans. y (c,– x)e* + (c2 + xels Ans. y = ce 2 + (c2 + x)e/2 + te. Ans. y c, + c2 x + (C3 + C4 x + Cs x + 2x)ez %3D %3D + (c3 +caxe- Ans. y = c, cos 4x + c2 sin 4x + 2 cos 3x. Ans. y = c, cos x + c2 sin x- sin 3x. 3r) cos 4x + c, sin 4x. Ans. y = (c, + c2 x + x)e3* . (D² + 16)y = 14 cos 3x. (4D? + 1)y = 35 sin 3x. %3D %3D
Transcribed Image Text:(D2 + 36)y = sin 6x. . (D2 + 9)y = sin 3x. %3D %3D L (D2 + 36)y = cos 6x. 4x Ans. y = C1e** + Cz e* + 2e?z Ans. y = c,e* + Cze' Ans. y C1e**+ (c2 + 3xje* Ans. y = ce*+ (C2- 4x)e xe* + (c2 + x)e" %3D . (D² + 3D - 4)y = 12e2x. . (D² + 3D-4)y 21e3* (D? + 3D - 4)y (D? + 3D - 4)y 20e,4x. (D² - 3D + 2)y = e + e2x. (4D2 - 1)y = e/2 + 12e. E D(D – 2)y = 48e2. E (D - 18D2 + 81)y = 36e3*. + te. %3D -4x 15e. 1 Ans. y (c,– x)e* + (c2 + xels Ans. y = ce 2 + (c2 + x)e/2 + te. Ans. y c, + c2 x + (C3 + C4 x + Cs x + 2x)ez %3D %3D + (c3 +caxe- Ans. y = c, cos 4x + c2 sin 4x + 2 cos 3x. Ans. y = c, cos x + c2 sin x- sin 3x. 3r) cos 4x + c, sin 4x. Ans. y = (c, + c2 x + x)e3* . (D² + 16)y = 14 cos 3x. (4D? + 1)y = 35 sin 3x. %3D %3D
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