According to the theorem these should form a fundament set of solutions. This is easy enough to check. This is not a problem. There are an infinite number of pairs of functions that we could use as a fundamental set of solutions for this problem. So, which set of fundamental solutions should we use?
Well, if we use the ones that we originally found, the general solution would be,. This would not be very fun to work with when it came to determining the coefficients to satisfy a general set of initial conditions. We should always try to use the set that is the most convenient to use for a given problem.
An Introduction to the Fundamentals
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Solution of Differential Equations with Applications to Engineering Problems
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