Updates:
Labels: NeedsBetterPatch
Comment #18 on issue 1261 by asmeurer: incorrect exponentiation with
non-commutative symbols
http://code.google.com/p/sympy/issues/detail?id=1261
The ODE fail is a strange one:
Old:
In [12]: dsolve(Eq(x*f(x).diff(x) + f(x) - f(x)**2,0), f(x), "Bernoulli")
Out[12]:
1
f(x) = ──────────
⎛ 1⎞
x⋅⎜C₁ + ─⎟
⎝ x⎠
In [3]: dsolve(Eq(x*f(x).diff(x) + f(x) - f(x)**2,0),
f(x), "Bernoulli_Integral")
Out[3]:
⌠
⎮ 1
-⎮ ─ dx
⎮ x
⌡
ℯ
f(x) = ───────────────────
⌠
⎮ ⌠
⎮ ⎮ 1
⎮ -⎮ ─ dx
⎮ ⎮ x
⎮ ⌡
⎮ -ℯ
C₁ + ⎮ ───────── dx
⎮ x
⌡
In [24]: Eq(f(x), exp(-integrate(1/x, x))/(C1 +
integrate(-exp(-integrate(1/x, x))/x, x)))
Out[24]:
1
f(x) = ──────────
⎛ 1⎞
x⋅⎜C₁ + ─⎟
⎝ x⎠
Your patch:
In [14]: dsolve(Eq(x*f(x).diff(x) + f(x) - f(x)**2,0), f(x), "Bernoulli")
Out[14]: f(x) = 1
In [15]: dsolve(Eq(x*f(x).diff(x) + f(x) - f(x)**2,0),
f(x), "Bernoulli_Integral")
Out[15]: f(x) = 1
In [24]: Eq(f(x), exp(-integrate(1/x, x))/(C1 +
integrate(-exp(-integrate(1/x, x))/x, x)))
Out[24]:
1
f(x) = ──────────
⎛ 1⎞
x⋅⎜C₁ + ─⎟
⎝ x⎠
Also, your patch has a whitespace error.
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