# Differential equations DSolve constant issue

After using DSolve to a set of differential equations, three constants arise. They are C[1], C[2] and C[21]. I have checked thoroughly that there are no C[3], C[4],....C[20]. It is quite mysterious to me as normally the constants are in numerical order. Is there any relationship between C[21] and C[1] or C[2]? Thank you very much.

• Can you provide your differential equations? Feb 18, 2015 at 21:28
• @bill It looks like the poster knows this. The issue seems to be the occurrence of a C[21] instead of the expected C[3]. Feb 18, 2015 at 23:25
• Probably the other ones were used and then discarded. There should be no relationship between C[21] and C[1] and C[2]. (That's really a wild guess, since it's impossible to know without code that reproduces the problem.) It's also possible that you already have definitions for C[3] through C[20]. Feb 19, 2015 at 0:13
• My differential equations (DAEs) are too long. They are 40 equations. Yet 20 of them are coupled to each other and the other 20 coupled to the other 20. It is also expected that in the first set (the first 20), there are two constants. For another set (the other 20), there is one constant. Is this the reason why the third constant is named C[21] but not C[3]? There are 3 differential equations in these 40 DAEs; they are located in the first, seventh and the twenty-first equation. Feb 19, 2015 at 1:07
• I have pasted my complete example on mathematica.stackexchange.com/questions/75845/… Any help on the relation between C[21] with C[1] and C[2] is very appreciated. Feb 25, 2015 at 6:46

According to the documentation for GeneratedParameters:
• The typical default setting is GeneratedParameters -> C.
• The setting GeneratedParameters -> f specifies that successive generated parameters should be named f[1], f[2], …
• In typical cases, the f[i] are used to parameterize families of solutions to equations.
• The f[i] usually correspond to free parameters, but are also sometimes used to represent arbitrary functions.
• The f[i] have indices that start at 1 for each invocation of a particular symbolic operation.