\[ \left \{a t x'(t)=b c (y(t)-z(t)),b t y'(t)=a c (z(t)-x(t)),c t z'(t)=a b (x(t)-y(t))\right \} \] ✗ Mathematica : cpu = 0.0210641 (sec), leaf count = 0 , could not solve
DSolve[{a*t*Derivative[1][x][t] == b*c*(y[t] - z[t]), b*t*Derivative[1][y][t] == a*c*(-x[t] + z[t]), c*t*Derivative[1][z][t] == a*b*(x[t] - y[t])}, {x[t], y[t], z[t]}, t]
✓ Maple : cpu = 0.215 (sec), leaf count = 308
\[ \left \{ \left \{ x \left ( t \right ) ={\it \_C1}+{\it \_C2}\,\sin \left ( \sqrt {{a}^{2}+{b}^{2}+{c}^{2}}\ln \left ( t \right ) \right ) +{\it \_C3}\,\cos \left ( \sqrt {{a}^{2}+{b}^{2}+{c}^{2}}\ln \left ( t \right ) \right ) ,y \left ( t \right ) ={\frac {1}{b \left ( {b}^{2}+{c}^{2} \right ) } \left ( {\it \_C1}\,{b}^{3}+ \left ( \left ( -{\it \_C3}\,\cos \left ( \sqrt {{a}^{2}+{b}^{2}+{c}^{2}}\ln \left ( t \right ) \right ) -{\it \_C2}\,\sin \left ( \sqrt {{a}^{2}+{b}^{2}+{c}^{2}}\ln \left ( t \right ) \right ) \right ) {a}^{2}+{c}^{2}{\it \_C1} \right ) b+a \left ( \cos \left ( \sqrt {{a}^{2}+{b}^{2}+{c}^{2}}\ln \left ( t \right ) \right ) {\it \_C2}-\sin \left ( \sqrt {{a}^{2}+{b}^{2}+{c}^{2}}\ln \left ( t \right ) \right ) {\it \_C3} \right ) c\sqrt {{a}^{2}+{b}^{2}+{c}^{2}} \right ) },z \left ( t \right ) ={\frac {1}{ \left ( {b}^{2}+{c}^{2} \right ) c} \left ( \sin \left ( \sqrt {{a}^{2}+{b}^{2}+{c}^{2}}\ln \left ( t \right ) \right ) \sqrt {{a}^{2}+{b}^{2}+{c}^{2}}{\it \_C3}\,ab-\sin \left ( \sqrt {{a}^{2}+{b}^{2}+{c}^{2}}\ln \left ( t \right ) \right ) {\it \_C2}\,{a}^{2}c-\cos \left ( \sqrt {{a}^{2}+{b}^{2}+{c}^{2}}\ln \left ( t \right ) \right ) \sqrt {{a}^{2}+{b}^{2}+{c}^{2}}{\it \_C2}\,ab-\cos \left ( \sqrt {{a}^{2}+{b}^{2}+{c}^{2}}\ln \left ( t \right ) \right ) {\it \_C3}\,{a}^{2}c+{\it \_C1}\,{b}^{2}c+{\it \_C1}\,{c}^{3} \right ) } \right \} \right \} \]