2.1916   ODE No. 1916

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

$$\{x^{\prime }(t)=h(a-x(t))(c-x(t)-y(t)),y^{\prime }(t)=k(b-y(t))(c-x(t)-y(t))\}$$ ✓ Mathematica : cpu = 0.339965 (sec), leaf count = 557

$$\left\{\{y(t)\to b(ah-h\text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{(h(a-K[1]){)}^{\frac{k}{h}}}{(a-K[1])(c_1(ah-hK[1]{)}^{\frac{k}{h}}(h(a-K[1]){)}^{\frac{k}{h}}-c(h(a-K[1]){)}^{\frac{k}{h}}+K[1](h(a-K[1]){)}^{\frac{k}{h}}+b(ah-hK[1]{)}^{\frac{k}{h}})}dK[1]\mathrm{\&}][c_2-ht]){}^{\frac{k}{h}}\left(h(a-\text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{(h(a-K[1]){)}^{\frac{k}{h}}}{(a-K[1])(c_1(ah-hK[1]{)}^{\frac{k}{h}}(h(a-K[1]){)}^{\frac{k}{h}}-c(h(a-K[1]){)}^{\frac{k}{h}}+K[1](h(a-K[1]){)}^{\frac{k}{h}}+b(ah-hK[1]{)}^{\frac{k}{h}})}dK[1]\mathrm{\&}][c_2-ht])\right){}^{-\frac{k}{h}}+c_1(ah-h\text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{(h(a-K[1]){)}^{\frac{k}{h}}}{(a-K[1])(c_1(ah-hK[1]{)}^{\frac{k}{h}}(h(a-K[1]){)}^{\frac{k}{h}}-c(h(a-K[1]){)}^{\frac{k}{h}}+K[1](h(a-K[1]){)}^{\frac{k}{h}}+b(ah-hK[1]{)}^{\frac{k}{h}})}dK[1]\mathrm{\&}][c_2-ht]){}^{\frac{k}{h}},x(t)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{(h(a-K[1]){)}^{\frac{k}{h}}}{(a-K[1])(c_1(ah-hK[1]{)}^{\frac{k}{h}}(h(a-K[1]){)}^{\frac{k}{h}}-c(h(a-K[1]){)}^{\frac{k}{h}}+K[1](h(a-K[1]){)}^{\frac{k}{h}}+b(ah-hK[1]{)}^{\frac{k}{h}})}dK[1]\mathrm{\&}][c_2-ht]\}\right\}$$ ✓ Maple : cpu = 0.333 (sec), leaf count = 180

$$\{[\{x\left(t\right)=a\},\{y\left(t\right)=\frac{(c-a){\mathrm{e}}^{k(t+\mathit{\_}\mathit{C}\mathit{1})(-c+a+b)}-b}{-1+{\mathrm{e}}^{k(t+\mathit{\_}\mathit{C}\mathit{1})(-c+a+b)}}\}],[\{x\left(t\right)=\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-{\int }^{\mathit{\_}\mathit{Z}}\frac{1}{\mathit{\_}\mathit{a}-a}{({(\mathit{\_}\mathit{a}-a)}^{-\frac{k}{h}}h\mathit{\_}\mathit{a}+{(\mathit{\_}\mathit{a}-a)}^{-\frac{k}{h}}hb-{(\mathit{\_}\mathit{a}-a)}^{-\frac{k}{h}}hc+\mathit{\_}\mathit{C}\mathit{1})}^{-1}{\left({(\mathit{\_}\mathit{a}-a)}^{\frac{k}{h}}\right)}^{-1}d\mathit{\_}\mathit{a}+t+\mathit{\_}\mathit{C}\mathit{2})\},\{y\left(t\right)=\frac{-\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)+{\left(x\left(t\right)\right)}^{2}h+(-a-c)hx\left(t\right)+ach}{h(a-x\left(t\right))}\}]\}$$