Consider the homogeneous second order linear equation

or the explicit one

Basic property:If Y₁ and Y₂ are two solutions, then

is also a solution for any arbitrary constants c₁c₂.

The natural question to ask is whether any solution y is equal to c₁y₁ + c₂y₂ for some c₁ and c₂.

The answer to this question uses the notion of linear independence of solutions.




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