Comment #11 on issue 3149 by smi...@gmail.com: solve() could attempt
logcombine when looking for solutions
http://code.google.com/p/sympy/issues/detail?id=3149
correction to comment 10 - solves with force=True
And the OP expressions behave as follows:
dsolve(2*x*f(x) + (x**2 + f(x)**2)*f(x).diff(x), f(x),
hint='1st_homogeneous
_coeff_best', simplify=True)
[f(x) == 2**(1/3)*(x**2/(C3 + sqrt(C4 + 4*x**6))**(1/3) - 2**(1/3)*(C1 +
sqrt(C2
+ 4*x**6))**(1/3)/2), f(x) == 2**(1/3)*(-2*x**2/(C1 + sqrt(C2 +
4*x**6))**(1/3)
+ 2**(1/3)*(-1 - sqrt(3)*I)*(C3 + sqrt(C4 + 4*x**6))**(1/3)/2)/(1 -
sqrt(3)*I),
f(x) == 2**(1/3)*(-2*x**2/(C1 + sqrt(C2 + 4*x**6))**(1/3) + 2**(1/3)*(-1 +
sqrt
(3)*I)*(C3 + sqrt(C4 + 4*x**6))**(1/3)/2)/(1 + sqrt(3)*I)]
dsolve(2*x*f(x) + (x**2 + f(x)**2)*f(x).diff(x), f(x),
hint='1st_homogeneous
_coeff_best', simplify=False)
log(f(x)) == log(C1) - log(3*x**2/f(x)**2 + 1)/3
solve(_,f(x))
[2**(1/3)*(x**2 - 2**(1/3)*(-C1**3 + sqrt(C1**6 +
4*x**6))**(2/3)/2)/(-C1**3 + s
qrt(C1**6 + 4*x**6))**(1/3), 2**(1/3)*(-8*x**2 + 2**(1/3)*(1 -
sqrt(3)*I)**2*(-C
1**3 + sqrt(C1**6 + 4*x**6))**(2/3))/(4*(1 - sqrt(3)*I)*(-C1**3 +
sqrt(C1**6 + 4
*x**6))**(1/3)), 2**(1/3)*(-8*x**2 + 2**(1/3)*(1 + sqrt(3)*I)**2*(-C1**3 +
sqrt(
C1**6 + 4*x**6))**(2/3))/(4*(1 + sqrt(3)*I)*(-C1**3 + sqrt(C1**6 +
4*x**6))**(1/
3))]
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