\[ \left \{a y'(t)+t x'(t)-x(t)+y'(t)^2=0,x'(t) y'(t)+t y'(t)-y(t)=0\right \} \] ✓ Mathematica : cpu = 0.0189121 (sec), leaf count = 31
\[\left \{\left \{x(t)\to a c_2+c_1 t+c_2{}^2,y(t)\to c_2 t+c_1 c_2\right \}\right \}\] ✓ Maple : cpu = 0.354 (sec), leaf count = 194
\[\left \{\left [\left \{x \left (t \right ) = -\frac {t^{2}}{3}\right \}, \left \{y \left (t \right ) = -\frac {t^{3}}{27 a}\right \}\right ], \left [\{x \left (t \right ) = c_{1} t +c_{2}\}, \left \{y \left (t \right ) = -\frac {\left (t +\frac {d}{d t}x \left (t \right )\right ) \left (t \left (\frac {d}{d t}x \left (t \right )\right )+\left (\frac {d}{d t}x \left (t \right )\right )^{2}-x \left (t \right )\right )}{a}\right \}\right ], \left [\left \{x \left (t \right ) = \frac {-3 c_{1}^{2} t^{2}-2 c_{1} \sqrt {3}\, t +3}{12 c_{1}^{2}}, x \left (t \right ) = \frac {-3 c_{1}^{2} t^{2}+2 c_{1} \sqrt {3}\, t +3}{12 c_{1}^{2}}, x \left (t \right ) = \frac {c_{1}^{2}}{4}-\frac {c_{1} \sqrt {3}\, t}{6}-\frac {t^{2}}{4}, x \left (t \right ) = \frac {c_{1}^{2}}{4}+\frac {c_{1} \sqrt {3}\, t}{6}-\frac {t^{2}}{4}\right \}, \left \{y \left (t \right ) = \frac {2 t^{3}+7 t x \left (t \right )+\left (2 t^{2}+6 x \left (t \right )\right ) \left (\frac {d}{d t}x \left (t \right )\right )}{9 a}\right \}\right ]\right \}\]