2.1926   ODE No. 1926

1. Problem in Latex
2. Mathematica input
3. Maple input

$$\{x(t)=f(x^{\prime }(t),y^{\prime }(t))+t{x}^{\prime }(t),y(t)=g(x^{\prime }(t),y^{\prime }(t))+t{y}^{\prime }(t)\}$$ ✗ Mathematica : cpu = 0.0059757 (sec), leaf count = 0 , could not solve

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]

✓ Maple : cpu = 0.333 (sec), leaf count = 96

$$\{[\{\int \mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(t\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)+g(\mathit{\_}\mathit{Z},\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right))-y\left(t\right))\mathrm{d}t+\mathit{\_}\mathit{C}\mathit{1}=t\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(t\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)+g(\mathit{\_}\mathit{Z},\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right))-y\left(t\right))+f(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(t\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)+g(\mathit{\_}\mathit{Z},\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right))-y\left(t\right)),\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right))\},\{x\left(t\right)=\int \mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(t\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)+g(\mathit{\_}\mathit{Z},\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right))-y\left(t\right))\mathrm{d}t+\mathit{\_}\mathit{C}\mathit{1}\}]\}$$