y" +3y+Ay=0, y'(0) =0, y'(x)=0
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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How can I find the Eigen values and Eigen vector of the given Eigen value problem?
![This differential equation represents a second-order linear homogeneous differential equation with constant coefficients and is given by:
\[ y'' + 3y' + \lambda y = 0 \]
Additionally, the equation is subject to the initial conditions:
\[ y'(0) = 0 \]
\[ y'(\pi) = 0 \]
Here, \( y \) is a function of \( x \), \( y' \) denotes the first derivative of \( y \) with respect to \( x \), and \( y'' \) denotes the second derivative of \( y \) with respect to \( x \). The parameter \( \lambda \) is a constant that may affect the nature of the solutions.
The initial conditions specify that the first derivative of \( y \) at \( x = 0 \) and \( x = \pi \) is zero.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab6a44fb-472d-4115-ae99-90593ad92ba0%2F956ea2c8-dc87-487e-8376-4a4c58f33e8e%2Ftsts0y_processed.png&w=3840&q=75)
Transcribed Image Text:This differential equation represents a second-order linear homogeneous differential equation with constant coefficients and is given by:
\[ y'' + 3y' + \lambda y = 0 \]
Additionally, the equation is subject to the initial conditions:
\[ y'(0) = 0 \]
\[ y'(\pi) = 0 \]
Here, \( y \) is a function of \( x \), \( y' \) denotes the first derivative of \( y \) with respect to \( x \), and \( y'' \) denotes the second derivative of \( y \) with respect to \( x \). The parameter \( \lambda \) is a constant that may affect the nature of the solutions.
The initial conditions specify that the first derivative of \( y \) at \( x = 0 \) and \( x = \pi \) is zero.
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