\[ \left \{x(t)=f\left (x'(t),y'(t)\right )+t x'(t),y(t)=g\left (x'(t),y'(t)\right )+t y'(t)\right \} \] ✓ Mathematica : cpu = 0.0055711 (sec), leaf count = 28
\[\{\{x(t)\to f(c_1,c_2)+c_1 t,y(t)\to g(c_1,c_2)+c_2 t\}\}\] ✓ Maple : cpu = 0.211 (sec), leaf count = 96
\[[\{\int \RootOf \left (g \left (\textit {\_Z} , \frac {d}{d t}y \relax (t )\right )-y \relax (t )+t \left (\frac {d}{d t}y \relax (t )\right )\right )d t +c_{1} = t \RootOf \left (g \left (\textit {\_Z} , \frac {d}{d t}y \relax (t )\right )-y \relax (t )+t \left (\frac {d}{d t}y \relax (t )\right )\right )+f \left (\RootOf \left (g \left (\textit {\_Z} , \frac {d}{d t}y \relax (t )\right )-y \relax (t )+t \left (\frac {d}{d t}y \relax (t )\right )\right ), \frac {d}{d t}y \relax (t )\right )\}, \{x \relax (t ) = \int \RootOf \left (g \left (\textit {\_Z} , \frac {d}{d t}y \relax (t )\right )-y \relax (t )+t \left (\frac {d}{d t}y \relax (t )\right )\right )d t +c_{1}\}]\]