2.1918   ODE No. 1918

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

$$\{x^{\prime }(t)=-x(t)y(t{)}^2+x(t)+y(t),y^{\prime }(t)=x(t{)}^{2}y(t)-x(t)-y(t)\}$$ ✗ Mathematica : cpu = 0.281872 (sec), leaf count = 0 , could not solve

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

✓ Maple : cpu = 2.128 (sec), leaf count = 182

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