Concept explainers
Additional Problems
Verify that
Write the general solution to the system
To verify:
That
Answer to Problem 1AP
Solution:
The general solution of the system is
Explanation of Solution
Given:
The solutions are given as,
Approach:
If Wronskian of the solutions is non zero, then the solutions are linearly independent on any interval.
The general solution to the system is given as,
Calculation:
Differentiate the given functions with respect to
Find
Find
Since,
Find the Wronskian of the solutions.
Here, the Wronskian is nonzero, the solutions are linearly independent on any interval.
Find the general solution to the system.
Therefore, the general solution of the system is
Conclusion:
Hence, the general solution of the system is
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Chapter 9 Solutions
Differential Equations and Linear Algebra (4th Edition)
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