Give the form of a particular solution of the differential equation -2x y"- 2y'- 8y =2 cos( 3 x) – 3 e2*- 3 z=A cos(3x) + Ce 4* *+Ex -2x b) z=A cos( 3x) + Bxe +C z=A cos(3x) + B sin(3x) + Ce -2x +E -2x d) z=A cos( 3x) + Be -2x +Ex z=A cos( 3x) + B sin(3x) + Ce f) O None of the above.
Give the form of a particular solution of the differential equation -2x y"- 2y'- 8y =2 cos( 3 x) – 3 e2*- 3 z=A cos(3x) + Ce 4* *+Ex -2x b) z=A cos( 3x) + Bxe +C z=A cos(3x) + B sin(3x) + Ce -2x +E -2x d) z=A cos( 3x) + Be -2x +Ex z=A cos( 3x) + B sin(3x) + Ce 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
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![**Title: Particular Solution of a Differential Equation**
**Problem Statement:**
Give the form of a particular solution of the differential equation:
\[ y'' - 2y' - 8y = 2 \cos(3x) - 3 e^{-2x} - 3 \]
**Options:**
a) \( z = A \cos(3x) + C e^{-2x} + Ex \)
b) \( z = A \cos(3x) + B x e^{-2x} + C \)
c) \( z = A \cos(3x) + B \sin(3x) + C e^{-2x} + E \)
d) \( z = A \cos(3x) + B e^{-2x} + C \)
e) \( z = A \cos(3x) + B \sin(3x) + C e^{-2x} + E x \)
f) None of the above.
**Instructions:**
Evaluate each option and choose the form that correctly represents a particular solution to the given differential equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88afae02-80d5-49da-ad82-a7933e6f4445%2F656b2386-3f24-4f39-9279-9109b7da8b92%2Fmefsc2r_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Particular Solution of a Differential Equation**
**Problem Statement:**
Give the form of a particular solution of the differential equation:
\[ y'' - 2y' - 8y = 2 \cos(3x) - 3 e^{-2x} - 3 \]
**Options:**
a) \( z = A \cos(3x) + C e^{-2x} + Ex \)
b) \( z = A \cos(3x) + B x e^{-2x} + C \)
c) \( z = A \cos(3x) + B \sin(3x) + C e^{-2x} + E \)
d) \( z = A \cos(3x) + B e^{-2x} + C \)
e) \( z = A \cos(3x) + B \sin(3x) + C e^{-2x} + E x \)
f) None of the above.
**Instructions:**
Evaluate each option and choose the form that correctly represents a particular solution to the given differential equation.
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