Give the general solution of the differential equation 4x p"+4y'+ 20y =2 e** cos( 2x) 1 e** cos( 2x) + 1 e** sin (2 x) + cos( 2 x) C, + C, sin(4 x) 4x a) O y= 30 4x 60 1 4x 1 4x b) O y =C, e"cos(2 x) + C, e** sin( 2 x) + e"cos( 2 x) + 30 e" sin(2x) 60 1 e** cos( 2x) 4x 4x c) O y=C, e*cos( 2 x) + C, e** sin(2x) 30 60 e" sin(2x) 1 1 e** sin (2 x) -2x -2x 4x 4x d) O y=C, e *cos(4 x) + C, e +C,e*sin(4x) + e" cos( 2 x) + 30 60 1 e*"cos( 2 x) 30 -2x 1 -2x sin(4 x) 4x 4x e) O y=C, e 4* cos(4 x) + C, e e" sin (2 x) 60 - f) O None of the above.
Give the general solution of the differential equation 4x p"+4y'+ 20y =2 e** cos( 2x) 1 e** cos( 2x) + 1 e** sin (2 x) + cos( 2 x) C, + C, sin(4 x) 4x a) O y= 30 4x 60 1 4x 1 4x b) O y =C, e"cos(2 x) + C, e** sin( 2 x) + e"cos( 2 x) + 30 e" sin(2x) 60 1 e** cos( 2x) 4x 4x c) O y=C, e*cos( 2 x) + C, e** sin(2x) 30 60 e" sin(2x) 1 1 e** sin (2 x) -2x -2x 4x 4x d) O y=C, e *cos(4 x) + C, e +C,e*sin(4x) + e" cos( 2 x) + 30 60 1 e*"cos( 2 x) 30 -2x 1 -2x sin(4 x) 4x 4x e) O y=C, e 4* cos(4 x) + C, e e" sin (2 x) 60 - f) O None of the above.
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 Statement:**
Give the general solution of the differential equation
\[ y'' + 4y' + 20y = 2e^{4x} \cos(2x) \]
**Options:**
a) \( y = \frac{1}{30} e^{4x} \cos(2x) + \frac{1}{60} e^{4x} \sin(2x) + \cos(2x)C_1 + C_2 \sin(4x) \)
b) \( y = C_1 e^{4x} \cos(2x) + C_2 e^{4x} \sin(2x) + \frac{1}{30} e^{4x} \cos(2x) + \frac{1}{60} e^{4x} \sin(2x) \)
c) \( y = C_1 e^{4x} \cos(2x) + C_2 e^{4x} \sin(2x) - \frac{1}{30} e^{4x} \cos(2x) - \frac{1}{60} e^{4x} \sin(2x) \)
d) \( y = C_1 e^{-2x} \cos(4x) + C_2 e^{-2x} \sin(4x) + \frac{1}{30} e^{4x} \cos(2x) + \frac{1}{60} e^{4x} \sin(2x) \)
e) \( y = C_1 e^{-2x} \cos(4x) + C_2 e^{-2x} \sin(4x) - \frac{1}{30} e^{4x} \cos(2x) - \frac{1}{60} e^{4x} \sin(2x) \)
f) None of the above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88afae02-80d5-49da-ad82-a7933e6f4445%2F85e79156-1a87-455b-ac19-4d334e2dc979%2Fyt26hz_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Give the general solution of the differential equation
\[ y'' + 4y' + 20y = 2e^{4x} \cos(2x) \]
**Options:**
a) \( y = \frac{1}{30} e^{4x} \cos(2x) + \frac{1}{60} e^{4x} \sin(2x) + \cos(2x)C_1 + C_2 \sin(4x) \)
b) \( y = C_1 e^{4x} \cos(2x) + C_2 e^{4x} \sin(2x) + \frac{1}{30} e^{4x} \cos(2x) + \frac{1}{60} e^{4x} \sin(2x) \)
c) \( y = C_1 e^{4x} \cos(2x) + C_2 e^{4x} \sin(2x) - \frac{1}{30} e^{4x} \cos(2x) - \frac{1}{60} e^{4x} \sin(2x) \)
d) \( y = C_1 e^{-2x} \cos(4x) + C_2 e^{-2x} \sin(4x) + \frac{1}{30} e^{4x} \cos(2x) + \frac{1}{60} e^{4x} \sin(2x) \)
e) \( y = C_1 e^{-2x} \cos(4x) + C_2 e^{-2x} \sin(4x) - \frac{1}{30} e^{4x} \cos(2x) - \frac{1}{60} e^{4x} \sin(2x) \)
f) None of the above.
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