Concept explainers
Prove Theorem 4.2.4 and Corollary 4.2.5.
Reduction of Order. Given one solution y, of a second order linear homogeneous equation,
a systematic procedure for deriving a second solution
To find a second solution, assume a solution of the form
Since
a first order equation for the function
This procedure is called the method of reduction of order, because the crucial step is the solution of a first order differential equation for
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Differential Equations: An Introduction to Modern Methods and Applications
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