2.1937   ODE No. 1937

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

$$\{x^{\prime }(t)=-x(t)y(t{)}^2+x(t)+y(t),y^{\prime }(t)=x(t{)}^{2}y(t)-x(t)-y(t),z^{\prime }(t)=y(t{)}^2-x(t{)}^2\}$$ ✗ Mathematica : cpu = 0.757668 (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], Derivative[1][z][t] == -x[t]^2 + y[t]^2}, {x[t], y[t], z[t]}, t]

✓ Maple : cpu = 1.039 (sec), leaf count = 242

$$\{[\{x\left(t\right)=0\},\{y\left(t\right)=0\},\{z\left(t\right)=c_1\}],[\{x\left(t\right)=\mathit{ODESolStruc}(\mathit{\text{\_a}},[\{\frac{4{\mathit{\text{\_a}}}^5+2{\mathit{\text{\_a}}}^2\mathit{\text{\_}}b\left(\mathit{\text{\_a}}\right)\left(\frac{d}{d\mathit{\text{\_a}}}\mathrm{\_}\mathrm{b}\left(\mathit{\text{\_a}}\right)\right)-3{\mathit{\text{\_a}}}^3-2\mathit{\text{\_a}}\mathit{\text{\_}}b{\left(\mathit{\text{\_a}}\right)}^2-\mathit{\text{\_a}}+(-4{\mathit{\text{\_a}}}^4+4{\mathit{\text{\_a}}}^2+1)\mathit{\text{\_}}b\left(\mathit{\text{\_a}}\right)+\sqrt{(4{\mathit{\text{\_a}}}^2-4\mathit{\text{\_a}}\mathit{\text{\_}}b\left(\mathit{\text{\_a}}\right)+1){({\mathit{\text{\_a}}}^3+\mathit{\text{\_a}}-\mathit{\text{\_}}b\left(\mathit{\text{\_a}}\right))}^2}}{2{\mathit{\text{\_a}}}^2}=0\},\{\mathit{\text{\_a}}=x\left(t\right),\mathit{\text{\_}}b\left(\mathit{\text{\_a}}\right)=\frac{d}{dt}x\left(t\right)\},\{t=c_2+\int \frac{1}{\mathit{\text{\_}}b\left(\mathit{\text{\_a}}\right)}d\mathit{\text{\_a}},x\left(t\right)=\mathit{\text{\_a}}\}])\},\{y\left(t\right)=\frac{\left(\frac{d^2}{d{t}^2}x\left(t\right)\right)x\left(t\right)+2(x{\left(t\right)}^3+\frac{\frac{d}{dt}x\left(t\right)}{2}-\frac{x\left(t\right)}{2})(-\frac{d}{dt}x\left(t\right)+x\left(t\right))}{x{\left(t\right)}^3-\frac{d}{dt}x\left(t\right)+x\left(t\right)}\},\{z\left(t\right)=c_1+\int \frac{-x{\left(t\right)}^5-2\left(\frac{d}{dt}x\left(t\right)\right)x{\left(t\right)}^2+2x{\left(t\right)}^3+\frac{d^2}{d{t}^2}x\left(t\right)}{x{\left(t\right)}^3-\frac{d}{dt}x\left(t\right)+x\left(t\right)}dt\}]\}$$