Give the general solution of the differential equation -5x y"+ 10y'+ 25 y =3xe a) O y=C, e*+ C,xe -Sx -5x хе 3 2 - 2 1 b) O y=C, e*+C,xe -5x -5x -5x e 2 3 c) O y=C, e*+ C,xe° -5x 3 -X + 5 d) O y=C, e*+C,xe+- -5x -5x -5x e 2 -5x 1 + xs- f O None of the above.
Give the general solution of the differential equation -5x y"+ 10y'+ 25 y =3xe a) O y=C, e*+ C,xe -Sx -5x хе 3 2 - 2 1 b) O y=C, e*+C,xe -5x -5x -5x e 2 3 c) O y=C, e*+ C,xe° -5x 3 -X + 5 d) O y=C, e*+C,xe+- -5x -5x -5x e 2 -5x 1 + xs- 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:
\[ y'' + 10y' + 25y = 3xe^{-5x} \]
**Options:**
a) \( y = C_1 e^{-5x} + C_2 xe^{-5x} - 3x - \frac{3}{2}x^2 \)
b) \( y = C_1 e^{-5x} + C_2 xe^{-5x} - \frac{1}{2} e^{-5x} x^3 \)
c) \( y = C_1 e^{-5x} + C_2 xe^{-5x} - 3x + \frac{3}{2}x^2 \)
d) \( y = C_1 e^{-5x} + C_2 xe^{-5x} + \frac{5}{2} e^{-5x} x^3 \)
e) \( y = C_1 e^{-5x} + C_2 xe^{-5x} + \frac{1}{2} e^{-5x} x^3 \)
f) None of the above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88afae02-80d5-49da-ad82-a7933e6f4445%2F32bcd2e3-ef4c-40bd-8f2f-54ab3cd50829%2F7uo47ir_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Give the general solution of the differential equation:
\[ y'' + 10y' + 25y = 3xe^{-5x} \]
**Options:**
a) \( y = C_1 e^{-5x} + C_2 xe^{-5x} - 3x - \frac{3}{2}x^2 \)
b) \( y = C_1 e^{-5x} + C_2 xe^{-5x} - \frac{1}{2} e^{-5x} x^3 \)
c) \( y = C_1 e^{-5x} + C_2 xe^{-5x} - 3x + \frac{3}{2}x^2 \)
d) \( y = C_1 e^{-5x} + C_2 xe^{-5x} + \frac{5}{2} e^{-5x} x^3 \)
e) \( y = C_1 e^{-5x} + C_2 xe^{-5x} + \frac{1}{2} e^{-5x} x^3 \)
f) None of the above.
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