This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.
 Mathematica Tutorial

# The GeneratedParameters Option

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 P[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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It is sometimes useful to display the solution using subscripts or other styles for the parameter indices.
Here, the parameters are named using subscripted variables.
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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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