Find a homogeneous linear differential equation with constant coefficients whose general solution is given. y = C₁ + C₂x + c3e5x y" + 5y" = 0 y" - 6y" + 5y' = 0 Oy"" - 5y" = 0 Oy"" + 5y' = 0 Oy"" + 6y" + 5y' = 0 X
Find a homogeneous linear differential equation with constant coefficients whose general solution is given. y = C₁ + C₂x + c3e5x y" + 5y" = 0 y" - 6y" + 5y' = 0 Oy"" - 5y" = 0 Oy"" + 5y' = 0 Oy"" + 6y" + 5y' = 0 X
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:**
Find a homogeneous linear differential equation with constant coefficients whose general solution is given.
**General Solution:**
\[ y = c_1 + c_2 x + c_3 e^{5x} \]
**Multiple Choice Options:**
- \( \circ \) \( y''' + 5y'' = 0 \)
- \( \bullet \) \( y''' - 6y'' + 5y' = 0 \)
- \( \circ \) \( y''' - 5y'' = 0 \)
- \( \circ \) \( y''' + 5y' = 0 \)
- \( \circ \) \( y''' + 6y'' + 5y' = 0 \)
**Explanation:**
The task is to identify the correct differential equation from the options given the general solution. The equation \( y''' - 6y'' + 5y' = 0 \) is the selected answer but marked incorrect, likely implying further analysis might be needed for the context of the problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F335131ff-484f-4768-821d-726b05458836%2Fa441d8ee-bce8-410e-b025-cb2e65b804d9%2F8s1l89b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find a homogeneous linear differential equation with constant coefficients whose general solution is given.
**General Solution:**
\[ y = c_1 + c_2 x + c_3 e^{5x} \]
**Multiple Choice Options:**
- \( \circ \) \( y''' + 5y'' = 0 \)
- \( \bullet \) \( y''' - 6y'' + 5y' = 0 \)
- \( \circ \) \( y''' - 5y'' = 0 \)
- \( \circ \) \( y''' + 5y' = 0 \)
- \( \circ \) \( y''' + 6y'' + 5y' = 0 \)
**Explanation:**
The task is to identify the correct differential equation from the options given the general solution. The equation \( y''' - 6y'' + 5y' = 0 \) is the selected answer but marked incorrect, likely implying further analysis might be needed for the context of the problem.
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