2.1925   ODE No. 1925

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

$$\{a{y}^{\prime }(t)+t{x}^{\prime }(t)-x(t)+y^{\prime }(t{)}^2=0,x^{\prime }(t)y^{\prime }(t)+t{y}^{\prime }(t)-y(t)=0\}$$ ✗ Mathematica : cpu = 8.47343 (sec), leaf count = 0 , could not solve

DSolve[{-x[t] + t*Derivative[1][x][t] + a*Derivative[1][y][t] + Derivative[1][y][t]^2 == 0, -y[t] + t*Derivative[1][y][t] + Derivative[1][x][t]*Derivative[1][y][t] == 0}, {x[t], y[t]}, t]

✓ Maple : cpu = 0.266 (sec), leaf count = 230

$$\{[\{x\left(t\right)=-\frac{t^2}{3}\},\{y\left(t\right)=-\frac{t^3}{27a}\}],[\{x\left(t\right)=\mathit{\_}\mathit{C}\mathit{1}t+\mathit{\_}\mathit{C}\mathit{2}\},\{y\left(t\right)=\frac{-{\left(\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)\right)}^3-2{\left(\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)\right)}^{2}t-\left(\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)\right)t^2+x\left(t\right)\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)+tx\left(t\right)}{a}\}],[\{x\left(t\right)=\frac{-2\mathit{\_}\mathit{C}\mathit{1}t(-\mathit{\_}\mathit{C}\mathit{1}t+\sqrt{3})-5{\mathit{\_}\mathit{C}\mathit{1}}^2{t}^2+3}{12{\mathit{\_}\mathit{C}\mathit{1}}^2},x\left(t\right)=\frac{2\mathit{\_}\mathit{C}\mathit{1}t(\mathit{\_}\mathit{C}\mathit{1}t+\sqrt{3})-5{\mathit{\_}\mathit{C}\mathit{1}}^2{t}^2+3}{12{\mathit{\_}\mathit{C}\mathit{1}}^2},x\left(t\right)=-\frac{5t^2}{12}-\frac{t(-t-\sqrt{3}\mathit{\_}\mathit{C}\mathit{1})}{6}+\frac{{\mathit{\_}\mathit{C}\mathit{1}}^2}{4},x\left(t\right)=-\frac{5t^2}{12}-\frac{t(-t+\sqrt{3}\mathit{\_}\mathit{C}\mathit{1})}{6}+\frac{{\mathit{\_}\mathit{C}\mathit{1}}^2}{4}\},\{y\left(t\right)=-\frac{-2\left(\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)\right)t^2-2t^3-6x\left(t\right)\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)-7tx\left(t\right)}{9a}\}]\}$$