Functions and Analysis

    

Exact Solution of ODEs - Vector Space Transformation Technique - Part 2

Authors: Claude Michael Cassano

Since the number of linearly independent solutions of an HLODE equals the order of the HLODE, the dimension of the solution set of an HLODE is it's order; so the dimension of all HLODEs of the same order is this order. Thus, a first order HLODE may be solved exactly using the single HLODE ; but higher order non-elementary HLODEs require that order number of equations to solve such HLODEs - i.e. usage of linear transformations between linearly independent HLODE solution sets of that same order. The first order HLODE being of dimension 1 may be solved exactly by itself. Higher order HLODEs are subject to condition that the additional dimensional HLODEs must also be satisfied.

Comments: 7 Pages. [Corrections made to conform with the requirements on the Submission Form]

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[v1] 2020-10-26 20:23:53

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