From what I've seen so far, the basis of the solution space for all the constant coefficient homo linear DE's have been linear combinations of the exponential function e or of some polynomial multiplied by the exponential function.(adsbygoogle = window.adsbygoogle || []).push({});

Is this always true that these DE's always result in solutions based on exponential, polynomial times exponential (and sin and cos combos)?

Is it ok to collapse all the sin and cos solutions into the space of exponential functions, since a complex component in the exponent gives cos and sin?

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# Soln space basis for all constant coeff homo linear DE's?

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