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I'm solving a system of ODEs using DSolve. I'm having a hard time keeping track of the number of undetermined constants that are still left in the solution. Is there a way to count or list the constants (C[1], C[2], etc.) that are present in a typical DSolve solution? This would give me a lot of insight into which boundary conditions I might need to supply, change or rethink, in order to solve for the constants.

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Maybe this will help:

sol = DSolve[{y'[x] == x^2 y[x], z'[x] == 5 z[x]}, {y[x], z[x]}, x]

{{y[x] -> E^(x^3/3) C[1], z[x] -> E^(5 x) C[2]}}

Cases[sol, C[x_] -> C[x], Infinity]

{C[1], C[2]}

or just

Cases[sol, C[_], Infinity]
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    $\begingroup$ Or just Cases[sol, C[_], Infinity]. In some cases you might want to add //Union $\endgroup$
    – Bob Hanlon
    Commented Oct 19, 2016 at 13:42

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