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A solution of is so the solutions of the following operator equal .
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and since is of order 1, M has the same order as L. As an example where the order of M is smaller than n1 * n2 (the respective orders of L1 and L2) consider L1 and L2 the following 2nd and 3rd order differential operators:
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The symmetric product of L1,L2 is not of order 6. It is of order 4, that is, equal to :
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The solution of M is the product of the solutions of L1 and L2; to see that let's compute first the solutions to L1 and L2 - formally - using DESol:
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