Homogeneous Linear Equations

Consider the homogeneous second order linear equation

displaymath11

or the explicit one

displaymath13

Basic property:If tex2html_wrap_inline15 and tex2html_wrap_inline17 are two solutions, then

displaymath19

is also a solution for any arbitrary constants tex2html_wrap_inline21 .

The natural question to ask is whether any solution y is equal to tex2html_wrap_inline25 for some tex2html_wrap_inline27 and tex2html_wrap_inline29.
The answer to this question uses the notion of linear independence of solutions.

[Differential Equations] [First Order D.E.] [Second Order D.E.]
[Geometry] [Algebra] [Trigonometry ]
[Calculus] [Complex Variables] [Matrix Algebra]

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Author: Mohamed Amine Khamsi

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