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In textbooks, it's often casually mentioned, without explanation, that any two solutions added together is the general solution, the form of every other solution.

I don't understand why this is or where that idea comes from. Can anyone explain why this is so?

EDIT: This question was badly put. I'm going to post another question that makes more sense. Thanks for the feedback.

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    Sometimes the general solution has the form $(C_0+C_1x)e^{\alpha x}$.2012-11-25

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