2.1915   ODE No. 1915

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

$$\{x^{\prime }(t)=x(t)(a(px(t)+qy(t))+\alpha ),y^{\prime }(t)=y(t)(b(px(t)+qy(t))+\beta )\}$$ ✗ Mathematica : cpu = 712.476 (sec), leaf count = 0 , could not solve

DSolve[{Derivative[1][x][t] == x[t]*(alpha + a*(p*x[t] + q*y[t])), Derivative[1][y][t] == y[t]*(beta + b*(p*x[t] + q*y[t]))}, {x[t], y[t]}, t]

✓ Maple : cpu = 9.982 (sec), leaf count = 181

$$\{[\{x\left(t\right)=0\},\{y\left(t\right)=\frac{\beta }{{\mathrm{e}}^{-\beta t}\mathit{\_}\mathit{C}\mathit{1}\beta -bq}\}],[\{x\left(t\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right),[\{{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^{-\frac{a+b}{a}}{\mathrm{e}}^{-\frac{(a\beta -\alpha b)\mathit{\_}\mathit{a}}{a}}\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)-\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^{-\frac{b}{a}}{\mathrm{e}}^{-\frac{(a\beta -\alpha b)\mathit{\_}\mathit{a}}{a}}ap-{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^{-\frac{b}{a}}{\mathrm{e}}^{-\frac{(a\beta -\alpha b)\mathit{\_}\mathit{a}}{a}}\alpha +\mathit{\_}\mathit{C}\mathit{1}=0\},\{\mathit{\_}\mathit{a}=t,\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=x\left(t\right)\},\{t=\mathit{\_}\mathit{a},x\left(t\right)=\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\}])\},\{y\left(t\right)=\frac{-{\left(x\left(t\right)\right)}^{2}ap-\alpha x\left(t\right)+\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)}{qx\left(t\right)a}\}]\}$$