2.1924   ODE No. 1924

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

$$\{(-t^2+x(t{)}^2+y(t{)}^2)x^{\prime }(t)=-2tx(t),(-t^2+x(t{)}^2+y(t{)}^2)y^{\prime }(t)=-2ty(t)\}$$ ✓ Mathematica : cpu = 0.0548189 (sec), leaf count = 191

$$\{\{y(t)\to \frac{c_1(e^{c_2}-\sqrt{-4t^2-4c_1{}^2{t}^2+e^{2c_2}})}{2(1+c_1{}^2)},x(t)\to \frac{e^{c_2}-\sqrt{-4t^2-4c_1{}^2{t}^2+e^{2c_2}}}{2(1+c_1{}^2)}\},\{y(t)\to \frac{c_1(\sqrt{-4t^2-4c_1{}^2{t}^2+e^{2c_2}}+e^{c_2})}{2(1+c_1{}^2)},x(t)\to \frac{\sqrt{-4t^2-4c_1{}^2{t}^2+e^{2c_2}}+e^{c_2}}{2(1+c_1{}^2)}\}\}$$ ✓ Maple : cpu = 0.679 (sec), leaf count = 180

$$\{[\{x\left(t\right)=0\},\{y\left(t\right)=\frac{1}{2\mathit{\_}\mathit{C}\mathit{1}}(1+\sqrt{-4{\mathit{\_}\mathit{C}\mathit{1}}^2{t}^2+1}),y\left(t\right)=\frac{1}{2\mathit{\_}\mathit{C}\mathit{1}}(1-\sqrt{-4{\mathit{\_}\mathit{C}\mathit{1}}^2{t}^2+1})\}],[\{x\left(t\right)=\frac{1}{2\mathit{\_}\mathit{C}\mathit{2}}(\mathit{\_}\mathit{C}\mathit{1}-\sqrt{-2\mathit{\_}\mathit{C}\mathit{2}{t}^2+{\mathit{\_}\mathit{C}\mathit{1}}^2}),x\left(t\right)=\frac{1}{2\mathit{\_}\mathit{C}\mathit{2}}(\mathit{\_}\mathit{C}\mathit{1}+\sqrt{-2\mathit{\_}\mathit{C}\mathit{2}{t}^2+{\mathit{\_}\mathit{C}\mathit{1}}^2})\},\{y\left(t\right)=\frac{1}{\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)}\sqrt{\left(\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)\right)((t^2-{\left(x\left(t\right)\right)}^2)\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)-2tx\left(t\right))},y\left(t\right)=-\frac{1}{\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)}\sqrt{\left(\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)\right)((t^2-{\left(x\left(t\right)\right)}^2)\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)-2tx\left(t\right))}\}]\}$$