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