\[ \left \{\left (-t^2+x(t)^2+y(t)^2\right ) x'(t)=-2 t x(t),\left (-t^2+x(t)^2+y(t)^2\right ) y'(t)=-2 t y(t)\right \} \] ✓ Mathematica : cpu = 0.0548189 (sec), leaf count = 191
\[\left \{\left \{y(t)\to \frac {c_1 \left (e^{c_2}-\sqrt {-4 t^2-4 c_1{}^2 t^2+e^{2 c_2}}\right )}{2 \left (1+c_1{}^2\right )},x(t)\to \frac {e^{c_2}-\sqrt {-4 t^2-4 c_1{}^2 t^2+e^{2 c_2}}}{2 \left (1+c_1{}^2\right )}\right \},\left \{y(t)\to \frac {c_1 \left (\sqrt {-4 t^2-4 c_1{}^2 t^2+e^{2 c_2}}+e^{c_2}\right )}{2 \left (1+c_1{}^2\right )},x(t)\to \frac {\sqrt {-4 t^2-4 c_1{}^2 t^2+e^{2 c_2}}+e^{c_2}}{2 \left (1+c_1{}^2\right )}\right \}\right \}\] ✓ Maple : cpu = 0.679 (sec), leaf count = 180
\[ \left \{ [ \left \{ x \left ( t \right ) =0 \right \} , \left \{ y \left ( t \right ) ={\frac {1}{2\,{\it \_C1}} \left ( 1+\sqrt {-4\,{{\it \_C1}}^{2}{t}^{2}+1} \right ) },y \left ( t \right ) ={\frac {1}{2\,{\it \_C1}} \left ( 1-\sqrt {-4\,{{\it \_C1}}^{2}{t}^{2}+1} \right ) } \right \} ],[ \left \{ x \left ( t \right ) ={\frac {1}{2\,{\it \_C2}} \left ( {\it \_C1}-\sqrt {-2\,{\it \_C2}\,{t}^{2}+{{\it \_C1}}^{2}} \right ) },x \left ( t \right ) ={\frac {1}{2\,{\it \_C2}} \left ( {\it \_C1}+\sqrt {-2\,{\it \_C2}\,{t}^{2}+{{\it \_C1}}^{2}} \right ) } \right \} , \left \{ y \left ( t \right ) ={\frac {1}{{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) }\sqrt { \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) \left ( \left ( {t}^{2}- \left ( x \left ( t \right ) \right ) ^{2} \right ) {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) -2\,tx \left ( t \right ) \right ) }},y \left ( t \right ) =-{\frac {1}{{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) }\sqrt { \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) \left ( \left ( {t}^{2}- \left ( x \left ( t \right ) \right ) ^{2} \right ) {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) -2\,tx \left ( t \right ) \right ) }} \right \} ] \right \} \]