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I was wondering if someone could provide either a bit of intuition or a mathematical proof (or both) as to why if the Wronskian (W(f,g)) does not equal 0 for all t in an interval, then the linear combinations of the two functions f and g encompass ALL solutions. Is there any particular reason that this can be known to include all possible solutions for the second order, linear, homogeneous differential equation?

Any insight would be greatly appreciated!

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# 2nd order, linear, homogeneous proof

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