Updates:
Blockedon: 1336
Comment #8 on issue 2219 by asmeurer: Arbitrary constants in indefinite
integration
http://code.google.com/p/sympy/issues/detail?id=2219
That's because integrate(0, y) == C_1(x), not C_1.
What is really needed is some way to say what the constants are constants
with respect to (instead of the reverse). And then it would be assumed
that they are not constant with respect to anything else in general. I
seem to remember suggesting this somewhere in the past, but I don't know
where it is by now.
But I agree that barring this kind of advanced functionality, which would
almost have to have a special object a la issue 1336,
integrate(constant=True) should just return a C (or C_n) term, and not a
function.
Also, I want to point out that in general, if you want to get arbitrary
constants, you should pass your function to dsolve() or pdesolve().
dsolve() at least can handle any ode of the form f(x).diff(x, n) = g(x) via
variation of parameters method, or even the very fast constant coefficients
method if g(x) has the right form. Of course, this requires converting the
integral into an ode/pde, which I think might be non-trivial at least in
the pde case.
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