\[ \left \{x(t)=f\left (x'(t),y'(t)\right )+t x'(t),y(t)=g\left (x'(t),y'(t)\right )+t y'(t)\right \} \] ✓ Mathematica : cpu = 0.0059445 (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 = 0.273 (sec), leaf count = 96
\[\{[\{c_{1}+\int \RootOf \left (t \left (\frac {d}{d t}y \left (t \right )\right )+g \left (\textit {\_Z} , \frac {d}{d t}y \left (t \right )\right )-y \left (t \right )\right )d t = t \RootOf \left (t \left (\frac {d}{d t}y \left (t \right )\right )+g \left (\textit {\_Z} , \frac {d}{d t}y \left (t \right )\right )-y \left (t \right )\right )+f \left (\RootOf \left (t \left (\frac {d}{d t}y \left (t \right )\right )+g \left (\textit {\_Z} , \frac {d}{d t}y \left (t \right )\right )-y \left (t \right )\right ), \frac {d}{d t}y \left (t \right )\right )\}, \{x \left (t \right ) = c_{1}+\int \RootOf \left (t \left (\frac {d}{d t}y \left (t \right )\right )+g \left (\textit {\_Z} , \frac {d}{d t}y \left (t \right )\right )-y \left (t \right )\right )d t\}]\}\]