Comment #6 on issue 1766 by asmeurer: expand(power_base=True) is too
aggressive
http://code.google.com/p/sympy/issues/detail?id=1766
Here is a slightly modified example that shows that even Maple ignores
assumptions on ODEs (Maple is usually a real stickler when it
comes to assumptions):
> dsolve(diff(f(x), x) = sqrt(f(x)**2*(x + 1)));
/2 (3/2)\
f(x) = exp|- (x + 1) | _C1
\3 /
> sqrt(f(x)**2);
(1/2)
/ 2\
\f(x) /
> int(1/sqrt(x**2), x);
x ln(x)
---------
(1/2)
/ 2\
\x /
Compare to us (right now):
In [16]: dsolve(diff(f(x), x) - sqrt(f(x)**2)*sqrt((x + 1)), f(x))
Out[16]:
f(x)
⌠ 3/2
⎮ 1 2⋅(1 + x)
⎮ ─────── dy = C₁ + ────────────
⎮ ⎽⎽⎽⎽ 3
⎮ ╱ 2
⎮ ╲╱ y
⌡
It seems we can't do that integral, but the point is that Maple just
ignores the fact that sqrt(f(x)**2) != f(x) when solving the ODE.
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