Concept explainers
Program Description: Purpose of problem is to determine whether
Explanation of Solution
Given information:
The second order differential equation is,
The value of first order differential equation at
The value of the function at
Explanation:
Consider
The characteristic equation can be expressed as follows,
The roots of the equation are as follows,
Therefore, the general solution of the differential equation can be expressed as,
Apply the initial condition in equation
Therefore, the value of
Since,
Now,consider
Then, the given differential equation can be expressed as follows,
The characteristic equation can be expressed as follows,
The roots of the equation are as follows,
Therefore, the general solution of the differential equation can be expressed as,
Differentiate the above equation with respect to
Apply the initial condition
Apply the initial condition
Therefore, the value of
Then the value of
Since,
Now,consider
Then, the given differential equation can be expressed as follows,
The characteristic equation can be expressed as follows,
The roots of the equation are as follows,
Therefore, the general solution of the differential equation can be expressed as,
Differentiate the above equation with respect to
Apply the initial condition
Apply the initial condition
Since, the value of
For all odd value
Hence, the eigenvalues for the given equation are as follows,
Conclusion:
Thus, the Eigen functions corresponding to the eigenvalues are
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Chapter 3 Solutions
Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
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