Give the general solution of the differential equation y"- 5y'+ 6y =x +3x 5 2 x+ 12 155 37 1 3 x + 216 36 155 b) O y-c, + C, - 5 2 216 36 12 6. 7 + 216 67 1 1 c) O y-C 36 12 67 d) O y=C, * + C,e* + 1 x+ 12 3x 216 36 331 125 13 2 5 e) O y=C, e* 216 36 6 f) O None of the above.
Give the general solution of the differential equation y"- 5y'+ 6y =x +3x 5 2 x+ 12 155 37 1 3 x + 216 36 155 b) O y-c, + C, - 5 2 216 36 12 6. 7 + 216 67 1 1 c) O y-C 36 12 67 d) O y=C, * + C,e* + 1 x+ 12 3x 216 36 331 125 13 2 5 e) O y=C, e* 216 36 6 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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![**Differential Equation Solution Options**
**Problem Statement:**
Determine the general solution of the differential equation:
\[ y'' - 5y' + 6y = x^{-3} + 3x \]
**Solution Options:**
a) \[ y = C_1 e^{2x} + C_2 e^{3x} + \frac{155}{216} + \frac{37}{36} x + \frac{5}{12} x^2 + \frac{1}{6} x^3 \]
b) \[ y = C_1 e^{2x} + C_2 e^{3x} - \frac{155}{216} - \frac{37}{36} x + \frac{5}{12} x^2 - \frac{1}{6} x^3 \]
c) \[ y = C_1 e^{2x} + C_2 e^{3x} - \frac{67}{216} + \frac{7}{36} x - \frac{1}{12} x^2 + \frac{1}{6} x^3 \]
d) \[ y = C_1 e^{2x} + C_2 e^{3x} + \frac{67}{216} - \frac{7}{36} x + \frac{1}{12} x^2 - \frac{1}{6} x^3 \]
e) \[ y = C_1 e^{2x} + C_2 e^{3x} - \frac{331}{216} + \frac{125}{36} x - \frac{13}{12} x^2 - \frac{5}{6} x^3 \]
f) None of the above.
Each option is a proposed solution to the given differential equation, where \( C_1 \) and \( C_2 \) are constants to be determined based on initial conditions or further information.
**Explanation of Components:**
- \( C_1 e^{2x} + C_2 e^{3x} \): Homogeneous solution to the differential equation.
- Terms like \(\frac{155}{216}\), \(\frac{37}{36} x\), etc., represent the particular solution to the differential equation based on the non-homogeneous part \(x^{-3} + 3x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88afae02-80d5-49da-ad82-a7933e6f4445%2F8cfc8c9d-4973-4c5b-8c00-bfd9ad35ebf8%2Faa9iyh_processed.png&w=3840&q=75)
Transcribed Image Text:**Differential Equation Solution Options**
**Problem Statement:**
Determine the general solution of the differential equation:
\[ y'' - 5y' + 6y = x^{-3} + 3x \]
**Solution Options:**
a) \[ y = C_1 e^{2x} + C_2 e^{3x} + \frac{155}{216} + \frac{37}{36} x + \frac{5}{12} x^2 + \frac{1}{6} x^3 \]
b) \[ y = C_1 e^{2x} + C_2 e^{3x} - \frac{155}{216} - \frac{37}{36} x + \frac{5}{12} x^2 - \frac{1}{6} x^3 \]
c) \[ y = C_1 e^{2x} + C_2 e^{3x} - \frac{67}{216} + \frac{7}{36} x - \frac{1}{12} x^2 + \frac{1}{6} x^3 \]
d) \[ y = C_1 e^{2x} + C_2 e^{3x} + \frac{67}{216} - \frac{7}{36} x + \frac{1}{12} x^2 - \frac{1}{6} x^3 \]
e) \[ y = C_1 e^{2x} + C_2 e^{3x} - \frac{331}{216} + \frac{125}{36} x - \frac{13}{12} x^2 - \frac{5}{6} x^3 \]
f) None of the above.
Each option is a proposed solution to the given differential equation, where \( C_1 \) and \( C_2 \) are constants to be determined based on initial conditions or further information.
**Explanation of Components:**
- \( C_1 e^{2x} + C_2 e^{3x} \): Homogeneous solution to the differential equation.
- Terms like \(\frac{155}{216}\), \(\frac{37}{36} x\), etc., represent the particular solution to the differential equation based on the non-homogeneous part \(x^{-3} + 3x
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