ODE No. 1926

$$\{x(t)=f(x^{\prime }(t),y^{\prime }(t))+t{x}^{\prime }(t),y(t)=g(x^{\prime }(t),y^{\prime }(t))+t{y}^{\prime }(t)\}$$ ✓ 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))})
 

$$[\{\int \mathrm{RootOf}(g(\mathit{\text{\_Z}},\frac{d}{dt}y\left(t\right))-y\left(t\right)+t\left(\frac{d}{dt}y\left(t\right)\right))dt+c_1=t\mathrm{RootOf}(g(\mathit{\text{\_Z}},\frac{d}{dt}y\left(t\right))-y\left(t\right)+t\left(\frac{d}{dt}y\left(t\right)\right))+f(\mathrm{RootOf}(g(\mathit{\text{\_Z}},\frac{d}{dt}y\left(t\right))-y\left(t\right)+t\left(\frac{d}{dt}y\left(t\right)\right)),\frac{d}{dt}y\left(t\right))\},\{x\left(t\right)=\int \mathrm{RootOf}(g(\mathit{\text{\_Z}},\frac{d}{dt}y\left(t\right))-y\left(t\right)+t\left(\frac{d}{dt}y\left(t\right)\right))dt+c_1\}]$$