Comment #12 on issue 3148 by smi...@gmail.com: Too many constants from
dsolve()
http://code.google.com/p/sympy/issues/detail?id=3148
And here's another simpler case where the numbering issue can be seen:
Here is a differential equation
eq
x**2*f(x)**2 + x*Derivative(f(x), x)
The implicit solution is ok
sol = dsolve(eq, hint = 'separable_reduced', simplify=False)
sol
log(x**2*f(x))/2 - log(x**2*f(x) - 2)/2 == C1 + log(x)
checkodesol(eq, sol, order=1, solve_for_func=False)
(True, 0)
If we solve for the solution explicitly, it is ok
fx = solve(sol, f(x), force=True); fx
[2*exp(2*C1)/(x**2*exp(2*C1) - 1)]
checkodesol(eq, fx[0], order=1, solve_for_func=False)
(True, 0)
But the constantsimp'ed form is not valid
constantsimp(fx[0], x, 2)
C1/(C1*x**2 - 1)
checkodesol(eq, _, order=1, solve_for_func=False)
(False, -C1**2*x**2)
If the solution is renumbered after constantsimp it becomes C1/(C2*x**2 -
1) and that solution doesn't check unless the right value of C2 is chosen
(C2 = C1/2)
checkodesol(eq, C1/(C2*x**2-1), order=1, solve_for_func=False)
(False, C1*x**2*(C1 - 2*C2))
If exp(2*C1) were simplified to C1 and the 2 not absorbed and the two C1s
not renumbered, the solution would have been validated:
checkodesol(eq, 2*C1/(C1*x**2-1), order=1, solve_for_func=False)
(True, 0)
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