Find the general solution of the nonhomogeneous equation y " - 3 y "+4 y ' – 12y =e + 2 1 3* + C, cos( 2 x) + C, sin ( 2 x) – - O -3x a) O y=C, 10 1 1 e* 10 -3x b) O y =C, e*+C, cos( 2 x) + C, sin ( 2 x) + 1 1 c) O y=C, e"+C, cos(2 x) + C, sin( 2 x) 10 1 1 e 10 -2x d) O y=C, e* + C, cos( 2 x) + C, sin(2 x) + e) O y=C, e+ C, cos( 2 x) + C, sin( 2 x) – - 1 1 e 3 f) O None of the above.
Find the general solution of the nonhomogeneous equation y " - 3 y "+4 y ' – 12y =e + 2 1 3* + C, cos( 2 x) + C, sin ( 2 x) – - O -3x a) O y=C, 10 1 1 e* 10 -3x b) O y =C, e*+C, cos( 2 x) + C, sin ( 2 x) + 1 1 c) O y=C, e"+C, cos(2 x) + C, sin( 2 x) 10 1 1 e 10 -2x d) O y=C, e* + C, cos( 2 x) + C, sin(2 x) + e) O y=C, e+ C, cos( 2 x) + C, sin( 2 x) – - 1 1 e 3 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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![**Problem: Find the General Solution**
Given the nonhomogeneous differential equation:
\[ y''' - 3y'' + 4y' - 12y = e^x + 2 \]
Select the correct general solution:
**Options:**
a) \( y = C_1 e^{-3x} + C_2 \cos(2x) + C_3 \sin(2x) - \frac{1}{6} - \frac{1}{10} e^x \)
b) \( y = C_1 e^{-3x} + C_2 \cos(2x) + C_3 \sin(2x) + \frac{1}{6} + \frac{1}{10} e^x \)
c) \( y = C_1 e^{3x} + C_2 \cos(2x) + C_3 \sin(2x) - \frac{1}{6} - \frac{1}{10} e^x \)
d) \( y = C_1 e^{-2x} + C_2 \cos(2x) + C_3 \sin(2x) + \frac{1}{6} + \frac{1}{10} e^x \)
e) \( y = C_1 e^{2x} + C_2 \cos(2x) + C_3 \sin(2x) - \frac{1}{3} - \frac{1}{5} e^x \)
f) None of the above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88afae02-80d5-49da-ad82-a7933e6f4445%2Fecd67132-b1a4-444e-a451-9756f453839b%2Fzh83m96_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem: Find the General Solution**
Given the nonhomogeneous differential equation:
\[ y''' - 3y'' + 4y' - 12y = e^x + 2 \]
Select the correct general solution:
**Options:**
a) \( y = C_1 e^{-3x} + C_2 \cos(2x) + C_3 \sin(2x) - \frac{1}{6} - \frac{1}{10} e^x \)
b) \( y = C_1 e^{-3x} + C_2 \cos(2x) + C_3 \sin(2x) + \frac{1}{6} + \frac{1}{10} e^x \)
c) \( y = C_1 e^{3x} + C_2 \cos(2x) + C_3 \sin(2x) - \frac{1}{6} - \frac{1}{10} e^x \)
d) \( y = C_1 e^{-2x} + C_2 \cos(2x) + C_3 \sin(2x) + \frac{1}{6} + \frac{1}{10} e^x \)
e) \( y = C_1 e^{2x} + C_2 \cos(2x) + C_3 \sin(2x) - \frac{1}{3} - \frac{1}{5} e^x \)
f) None of the above.
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