\[ \left \{\left (-t^2+x(t)^2+y(t)^2\right ) x'(t)=-2 t x(t),\left (-t^2+x(t)^2+y(t)^2\right ) y'(t)=-2 t y(t)\right \} \] ✓ Mathematica : cpu = 0.0720984 (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 = 0.391 (sec), leaf count = 180
\[\left \{\left [\{x \left (t \right ) = 0\}, \left \{y \left (t \right ) = \frac {1-\sqrt {-4 c_{1}^{2} t^{2}+1}}{2 c_{1}}, y \left (t \right ) = \frac {1+\sqrt {-4 c_{1}^{2} t^{2}+1}}{2 c_{1}}\right \}\right ], \left [\left \{x \left (t \right ) = \frac {c_{1}-\sqrt {-2 c_{2} t^{2}+c_{1}^{2}}}{2 c_{2}}, x \left (t \right ) = \frac {c_{1}+\sqrt {-2 c_{2} t^{2}+c_{1}^{2}}}{2 c_{2}}\right \}, \left \{y \left (t \right ) = \frac {\sqrt {\left (-2 t x \left (t \right )+\left (t^{2}-x \left (t \right )^{2}\right ) \left (\frac {d}{d t}x \left (t \right )\right )\right ) \left (\frac {d}{d t}x \left (t \right )\right )}}{\frac {d}{d t}x \left (t \right )}, y \left (t \right ) = -\frac {\sqrt {\left (-2 t x \left (t \right )+\left (t^{2}-x \left (t \right )^{2}\right ) \left (\frac {d}{d t}x \left (t \right )\right )\right ) \left (\frac {d}{d t}x \left (t \right )\right )}}{\frac {d}{d t}x \left (t \right )}\right \}\right ]\right \}\]