The GeneratedParameters Option

As previously discussed, the general solution to a differential equation contains undetermined coefficients that are labeled C[1], C[2], and so on.

This example has one undetermined parameter, C[1].

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To change the name of the undetermined parameter, use the GeneratedParameters option.

This changes the name of the undetermined coefficient to K[1].

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The parameter C should be thought of as a pure function that acts on a set of indices to generate different constants C[i].

This shows the behavior of C.

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Internally, the use of a pure function allows DSolve to increment the argument i in C[i] correctly for higher-order ODEs and systems of ODEs.

GeneratedParameters can be specified using a pure function.

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Using a pure function is particularly useful if you want to begin indexing the parameters at any value other than the default (1).

This uses a pure function to label the parameters in the previous example const[2] and const[3].

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Finally, with Module variables, you can get names for the parameters that are unique across different invocations of DSolve.

Here the same DSolve call generates different parameter names.

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