\[ \left \{(x(t)-y(t)) (x(t)-z(t)) x'(t)=f(t),(y(t)-x(t)) (y(t)-z(t)) y'(t)=f(t),(z(t)-x(t)) (z(t)-y(t)) z'(t)=f(t)\right \} \] ✗ Mathematica : cpu = 0.0303713 (sec), leaf count = 0 , could not solve
DSolve[{(x[t] - y[t])*(x[t] - z[t])*Derivative[1][x][t] == f[t], (-x[t] + y[t])*(y[t] - z[t])*Derivative[1][y][t] == f[t], (-x[t] + z[t])*(-y[t] + z[t])*Derivative[1][z][t] == f[t]}, {x[t], y[t], z[t]}, t]
✓ Maple : cpu = 1.524 (sec), leaf count = 899
\[ \left \{ [ \left \{ x \left ( t \right ) =\int \!-3\,{\frac {f \left ( t \right ) }{{{\it \_C1}}^{3}+11664\,{{\it \_C2}}^{2}-23328\,{\it \_C2}\,\int \!f \left ( t \right ) \,{\rm d}t+11664\, \left ( \int \!f \left ( t \right ) \,{\rm d}t \right ) ^{2}} \left ( \left ( -i\sqrt {3}+1 \right ) \left ( \left ( 1+108\,\sqrt {{\frac { \left ( \int \!f \left ( t \right ) \,{\rm d}t-{\it \_C2} \right ) ^{2}}{{{\it \_C1}}^{3}+11664\,{{\it \_C2}}^{2}-23328\,{\it \_C2}\,\int \!f \left ( t \right ) \,{\rm d}t+11664\, \left ( \int \!f \left ( t \right ) \,{\rm d}t \right ) ^{2}}}} \right ) \left ( {{\it \_C1}}^{3}+11664\,{{\it \_C2}}^{2}-23328\,{\it \_C2}\,\int \!f \left ( t \right ) \,{\rm d}t+11664\, \left ( \int \!f \left ( t \right ) \,{\rm d}t \right ) ^{2} \right ) ^{2} \right ) ^{2/3}+{\it \_C1}\, \left ( i\sqrt {3}+1 \right ) \left ( {{\it \_C1}}^{3}+11664\,{{\it \_C2}}^{2}-23328\,{\it \_C2}\,\int \!f \left ( t \right ) \,{\rm d}t+11664\, \left ( \int \!f \left ( t \right ) \,{\rm d}t \right ) ^{2} \right ) \right ) {\frac {1}{\sqrt [3]{ \left ( 1+108\,\sqrt {{\frac { \left ( \int \!f \left ( t \right ) \,{\rm d}t-{\it \_C2} \right ) ^{2}}{{{\it \_C1}}^{3}+11664\,{{\it \_C2}}^{2}-23328\,{\it \_C2}\,\int \!f \left ( t \right ) \,{\rm d}t+11664\, \left ( \int \!f \left ( t \right ) \,{\rm d}t \right ) ^{2}}}} \right ) \left ( {{\it \_C1}}^{3}+11664\,{{\it \_C2}}^{2}-23328\,{\it \_C2}\,\int \!f \left ( t \right ) \,{\rm d}t+11664\, \left ( \int \!f \left ( t \right ) \,{\rm d}t \right ) ^{2} \right ) ^{2}}}}}\,{\rm d}t+{\it \_C3},x \left ( t \right ) =\int \!3\,{\frac {f \left ( t \right ) }{{{\it \_C1}}^{3}+11664\,{{\it \_C2}}^{2}-23328\,{\it \_C2}\,\int \!f \left ( t \right ) \,{\rm d}t+11664\, \left ( \int \!f \left ( t \right ) \,{\rm d}t \right ) ^{2}} \left ( \left ( -i\sqrt {3}-1 \right ) \left ( \left ( 1+108\,\sqrt {{\frac { \left ( \int \!f \left ( t \right ) \,{\rm d}t-{\it \_C2} \right ) ^{2}}{{{\it \_C1}}^{3}+11664\,{{\it \_C2}}^{2}-23328\,{\it \_C2}\,\int \!f \left ( t \right ) \,{\rm d}t+11664\, \left ( \int \!f \left ( t \right ) \,{\rm d}t \right ) ^{2}}}} \right ) \left ( {{\it \_C1}}^{3}+11664\,{{\it \_C2}}^{2}-23328\,{\it \_C2}\,\int \!f \left ( t \right ) \,{\rm d}t+11664\, \left ( \int \!f \left ( t \right ) \,{\rm d}t \right ) ^{2} \right ) ^{2} \right ) ^{2/3}+{\it \_C1}\, \left ( {{\it \_C1}}^{3}+11664\,{{\it \_C2}}^{2}-23328\,{\it \_C2}\,\int \!f \left ( t \right ) \,{\rm d}t+11664\, \left ( \int \!f \left ( t \right ) \,{\rm d}t \right ) ^{2} \right ) \left ( i\sqrt {3}-1 \right ) \right ) {\frac {1}{\sqrt [3]{ \left ( 1+108\,\sqrt {{\frac { \left ( \int \!f \left ( t \right ) \,{\rm d}t-{\it \_C2} \right ) ^{2}}{{{\it \_C1}}^{3}+11664\,{{\it \_C2}}^{2}-23328\,{\it \_C2}\,\int \!f \left ( t \right ) \,{\rm d}t+11664\, \left ( \int \!f \left ( t \right ) \,{\rm d}t \right ) ^{2}}}} \right ) \left ( {{\it \_C1}}^{3}+11664\,{{\it \_C2}}^{2}-23328\,{\it \_C2}\,\int \!f \left ( t \right ) \,{\rm d}t+11664\, \left ( \int \!f \left ( t \right ) \,{\rm d}t \right ) ^{2} \right ) ^{2}}}}}\,{\rm d}t+{\it \_C3},x \left ( t \right ) =\int \!6\,{\frac {f \left ( t \right ) }{{{\it \_C1}}^{3}+11664\,{{\it \_C2}}^{2}-23328\,{\it \_C2}\,\int \!f \left ( t \right ) \,{\rm d}t+11664\, \left ( \int \!f \left ( t \right ) \,{\rm d}t \right ) ^{2}} \left ( {{\it \_C1}}^{4}+11664\, \left ( \int \!f \left ( t \right ) \,{\rm d}t \right ) ^{2}{\it \_C1}-23328\,\int \!f \left ( t \right ) \,{\rm d}t{\it \_C1}\,{\it \_C2}+11664\,{\it \_C1}\,{{\it \_C2}}^{2}+ \left ( \left ( 1+108\,\sqrt {{\frac { \left ( \int \!f \left ( t \right ) \,{\rm d}t-{\it \_C2} \right ) ^{2}}{{{\it \_C1}}^{3}+11664\,{{\it \_C2}}^{2}-23328\,{\it \_C2}\,\int \!f \left ( t \right ) \,{\rm d}t+11664\, \left ( \int \!f \left ( t \right ) \,{\rm d}t \right ) ^{2}}}} \right ) \left ( {{\it \_C1}}^{3}+11664\,{{\it \_C2}}^{2}-23328\,{\it \_C2}\,\int \!f \left ( t \right ) \,{\rm d}t+11664\, \left ( \int \!f \left ( t \right ) \,{\rm d}t \right ) ^{2} \right ) ^{2} \right ) ^{2/3} \right ) {\frac {1}{\sqrt [3]{ \left ( 1+108\,\sqrt {{\frac { \left ( \int \!f \left ( t \right ) \,{\rm d}t-{\it \_C2} \right ) ^{2}}{{{\it \_C1}}^{3}+11664\,{{\it \_C2}}^{2}-23328\,{\it \_C2}\,\int \!f \left ( t \right ) \,{\rm d}t+11664\, \left ( \int \!f \left ( t \right ) \,{\rm d}t \right ) ^{2}}}} \right ) \left ( {{\it \_C1}}^{3}+11664\,{{\it \_C2}}^{2}-23328\,{\it \_C2}\,\int \!f \left ( t \right ) \,{\rm d}t+11664\, \left ( \int \!f \left ( t \right ) \,{\rm d}t \right ) ^{2} \right ) ^{2}}}}}\,{\rm d}t+{\it \_C3} \right \} , \left \{ y \left ( t \right ) ={\frac {1}{4\, \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{3}} \left ( 4\, \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{3}x \left ( t \right ) + \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) \right ) f \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}f \left ( t \right ) \right ) {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) -\sqrt {-16\, \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{5}f \left ( t \right ) + \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) \right ) ^{2} \left ( f \left ( t \right ) \right ) ^{2}-2\, \left ( {\frac {\rm d}{{\rm d}t}}f \left ( t \right ) \right ) \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) \right ) f \left ( t \right ) + \left ( {\frac {\rm d}{{\rm d}t}}f \left ( t \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{2}} \right ) },y \left ( t \right ) ={\frac {1}{4\, \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{3}} \left ( 4\, \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{3}x \left ( t \right ) + \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) \right ) f \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}f \left ( t \right ) \right ) {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) +\sqrt {-16\, \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{5}f \left ( t \right ) + \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) \right ) ^{2} \left ( f \left ( t \right ) \right ) ^{2}-2\, \left ( {\frac {\rm d}{{\rm d}t}}f \left ( t \right ) \right ) \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) \right ) f \left ( t \right ) + \left ( {\frac {\rm d}{{\rm d}t}}f \left ( t \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{2}} \right ) } \right \} , \left \{ z \left ( t \right ) ={\frac {x \left ( t \right ) \left ( x \left ( t \right ) -y \left ( t \right ) \right ) {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) -f \left ( t \right ) }{ \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) \left ( x \left ( t \right ) -y \left ( t \right ) \right ) }} \right \} ] \right \} \]