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y" +3y+Ay=0, y'(0) =0, y'(x)=0

y" +3y+Ay=0, y'(0) =0, y'(x)=0

Advanced Engineering Mathematics
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.
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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