2.1920   ODE No. 1920

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

$$\{x^{\prime }(t)=x(t)(x(t{)}^2+y(t{)}^2-1)-y(t),y^{\prime }(t)=y(t)(x(t{)}^2+y(t{)}^2-1)+x(t)\}$$ ✗ Mathematica : cpu = 0.0828333 (sec), leaf count = 0 , could not solve

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

✓ Maple : cpu = 4.986 (sec), leaf count = 248

$$\{[\{x\left(t\right)=0\},\{y\left(t\right)=0\}],[\{x\left(t\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{a},[\{\left(\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+\frac{1}{2{\mathit{\_}\mathit{a}}^3}(-6{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2{\mathit{\_}\mathit{a}}^2-4\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right){\mathit{\_}\mathit{a}}^3+4{\mathit{\_}\mathit{a}}^4-6\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathit{\_}\mathit{a}-4{\mathit{\_}\mathit{a}}^2+\sqrt{-64{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2{\mathit{\_}\mathit{a}}^6-64\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right){\mathit{\_}\mathit{a}}^7-16{\mathit{\_}\mathit{a}}^8+64{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^3{\mathit{\_}\mathit{a}}^3+128{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2{\mathit{\_}\mathit{a}}^4+48\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right){\mathit{\_}\mathit{a}}^5+48{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2{\mathit{\_}\mathit{a}}^2+64\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right){\mathit{\_}\mathit{a}}^3+16{\mathit{\_}\mathit{a}}^4+12\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathit{\_}\mathit{a}+8{\mathit{\_}\mathit{a}}^2+1}-1)=0\},\{\mathit{\_}\mathit{a}=x\left(t\right),\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)\},\{t=\int {\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1},x\left(t\right)=\mathit{\_}\mathit{a}\}])\},\{y\left(t\right)=\frac{-3{\left(\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)\right)}^{2}x\left(t\right)-2\left(\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)\right){\left(x\left(t\right)\right)}^2+\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}x\left(t\right)\right){\left(x\left(t\right)\right)}^2+2{\left(x\left(t\right)\right)}^3-\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)-x\left(t\right)}{4x\left(t\right)\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)+2{\left(x\left(t\right)\right)}^2+1}\}]\}$$