2.1931   ODE No. 1931

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

$$\{a{x}^{\prime }(t)=(b-c)y(t)z(t),b{y}^{\prime }(t)=(c-a)x(t)z(t),c{z}^{\prime }(t)=(a-b)x(t)y(t)\}$$ ✓ Mathematica : cpu = 5.63777 (sec), leaf count = 1461

$$\{\{x(t)\to \frac{\sqrt{2}b\sqrt{a(a-c)}(c-b)c_1\text{sn}(\frac{\sqrt{2}\sqrt{a-c}\sqrt{b-c}\sqrt{c_2}(c_3-t)}{\sqrt{a}\sqrt{b}}|-\frac{(a-b)b{c}_1}{(a-c)c{c}_2})}{a(c-a)\sqrt{b(b-c)c_1}},y(t)\to -\frac{\sqrt{2}\sqrt{-b(b-c)c_1(\text{sn}(\frac{\sqrt{2}\sqrt{a-c}\sqrt{b-c}\sqrt{c_2}(c_3-t)}{\sqrt{a}\sqrt{b}}|-\frac{(a-b)b{c}_1}{(a-c)c{c}_2}){}^2-1)}}{\sqrt{b(b-c)}},z(t)\to \frac{\sqrt{2}\sqrt{\frac{(b-c)(b(b-a)c_1\text{sn}(\frac{\sqrt{2}\sqrt{a-c}\sqrt{b-c}\sqrt{c_2}(c_3-t)}{\sqrt{a}\sqrt{b}}|-\frac{(a-b)b{c}_1}{(a-c)c{c}_2}){}^2+c(c-a)c_2)}{c-a}}}{\sqrt{b-c}\sqrt{c}}\},\{x(t)\to \frac{\sqrt{2}b\sqrt{a(a-c)}(c-b)c_1\text{sn}(\frac{\sqrt{2}\sqrt{a-c}\sqrt{b-c}\sqrt{c_2}(c_3-t)}{\sqrt{a}\sqrt{b}}|-\frac{(a-b)b{c}_1}{(a-c)c{c}_2})}{a(c-a)\sqrt{b(b-c)c_1}},y(t)\to \frac{\sqrt{2}\sqrt{-b(b-c)c_1(\text{sn}(\frac{\sqrt{2}\sqrt{a-c}\sqrt{b-c}\sqrt{c_2}(c_3-t)}{\sqrt{a}\sqrt{b}}|-\frac{(a-b)b{c}_1}{(a-c)c{c}_2}){}^2-1)}}{\sqrt{b(b-c)}},z(t)\to -\frac{\sqrt{2}\sqrt{\frac{(b-c)(b(b-a)c_1\text{sn}(\frac{\sqrt{2}\sqrt{a-c}\sqrt{b-c}\sqrt{c_2}(c_3-t)}{\sqrt{a}\sqrt{b}}|-\frac{(a-b)b{c}_1}{(a-c)c{c}_2}){}^2+c(c-a)c_2)}{c-a}}}{\sqrt{b-c}\sqrt{c}}\},\{x(t)\to \frac{\sqrt{2}b\sqrt{a(a-c)}(c-b)c_1\text{sn}(\frac{\sqrt{2}\sqrt{a-c}\sqrt{b-c}\sqrt{c_2}(t-c_3)}{\sqrt{a}\sqrt{b}}|-\frac{(a-b)b{c}_1}{(a-c)c{c}_2})}{a(c-a)\sqrt{b(b-c)c_1}},y(t)\to -\frac{\sqrt{2}\sqrt{-b(b-c)c_1(\text{sn}(\frac{\sqrt{2}\sqrt{a-c}\sqrt{b-c}\sqrt{c_2}(t-c_3)}{\sqrt{a}\sqrt{b}}|-\frac{(a-b)b{c}_1}{(a-c)c{c}_2}){}^2-1)}}{\sqrt{b(b-c)}},z(t)\to -\frac{\sqrt{2}\sqrt{\frac{(b-c)(b(b-a)c_1\text{sn}(\frac{\sqrt{2}\sqrt{a-c}\sqrt{b-c}\sqrt{c_2}(t-c_3)}{\sqrt{a}\sqrt{b}}|-\frac{(a-b)b{c}_1}{(a-c)c{c}_2}){}^2+c(c-a)c_2)}{c-a}}}{\sqrt{b-c}\sqrt{c}}\},\{x(t)\to \frac{\sqrt{2}b\sqrt{a(a-c)}(c-b)c_1\text{sn}(\frac{\sqrt{2}\sqrt{a-c}\sqrt{b-c}\sqrt{c_2}(t-c_3)}{\sqrt{a}\sqrt{b}}|-\frac{(a-b)b{c}_1}{(a-c)c{c}_2})}{a(c-a)\sqrt{b(b-c)c_1}},y(t)\to \frac{\sqrt{2}\sqrt{-b(b-c)c_1(\text{sn}(\frac{\sqrt{2}\sqrt{a-c}\sqrt{b-c}\sqrt{c_2}(t-c_3)}{\sqrt{a}\sqrt{b}}|-\frac{(a-b)b{c}_1}{(a-c)c{c}_2}){}^2-1)}}{\sqrt{b(b-c)}},z(t)\to \frac{\sqrt{2}\sqrt{\frac{(b-c)(b(b-a)c_1\text{sn}(\frac{\sqrt{2}\sqrt{a-c}\sqrt{b-c}\sqrt{c_2}(t-c_3)}{\sqrt{a}\sqrt{b}}|-\frac{(a-b)b{c}_1}{(a-c)c{c}_2}){}^2+c(c-a)c_2)}{c-a}}}{\sqrt{b-c}\sqrt{c}}\}\}$$

✓ Maple : cpu = 0.861 (sec), leaf count = 1117

$$\{[\{x\left(t\right)=0\},\{y\left(t\right)=0\},\{z\left(t\right)=\mathit{\_}\mathit{C}\mathit{1}\}],[\{x\left(t\right)=0\},\{y\left(t\right)=\mathit{\_}\mathit{C}\mathit{1}\},\{z\left(t\right)=0\}],[\{x\left(t\right)=\mathit{\_}\mathit{C}\mathit{1}\},\{y\left(t\right)=0\},\{z\left(t\right)=0\}],[\{x\left(t\right)=\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-{\int }^{\mathit{\_}\mathit{Z}}-2\frac{bc(a-c)(a-b)}{\sqrt{bc(a-c)(a-b)(-4a^4{\mathit{\_}\mathit{a}}^4+8{\mathit{\_}\mathit{a}}^4{a}^{3}b+8{\mathit{\_}\mathit{a}}^4{a}^{3}c-4{\mathit{\_}\mathit{a}}^4{a}^2{b}^2-16{\mathit{\_}\mathit{a}}^4{a}^{2}bc-4{\mathit{\_}\mathit{a}}^4{a}^2{c}^2+8{\mathit{\_}\mathit{a}}^{4}a{b}^{2}c+8{\mathit{\_}\mathit{a}}^{4}ab{c}^2-4{\mathit{\_}\mathit{a}}^4{b}^2{c}^2+16\mathit{\_}\mathit{C}\mathit{2}{\mathit{\_}\mathit{a}}^2{a}^4-32\mathit{\_}\mathit{C}\mathit{2}{\mathit{\_}\mathit{a}}^2{a}^{3}b-32\mathit{\_}\mathit{C}\mathit{2}{\mathit{\_}\mathit{a}}^2{a}^{3}c+16\mathit{\_}\mathit{C}\mathit{2}{\mathit{\_}\mathit{a}}^2{a}^2{b}^2+64\mathit{\_}\mathit{C}\mathit{2}{\mathit{\_}\mathit{a}}^2{a}^{2}bc+16\mathit{\_}\mathit{C}\mathit{2}{\mathit{\_}\mathit{a}}^2{a}^2{c}^2-32\mathit{\_}\mathit{C}\mathit{2}{\mathit{\_}\mathit{a}}^{2}a{b}^{2}c-32\mathit{\_}\mathit{C}\mathit{2}{\mathit{\_}\mathit{a}}^{2}ab{c}^2+16\mathit{\_}\mathit{C}\mathit{2}{\mathit{\_}\mathit{a}}^2{b}^2{c}^2-16{\mathit{\_}\mathit{C}\mathit{2}}^2{a}^4+32{\mathit{\_}\mathit{C}\mathit{2}}^2{a}^{3}b+32{\mathit{\_}\mathit{C}\mathit{2}}^2{a}^{3}c-16{\mathit{\_}\mathit{C}\mathit{2}}^2{a}^2{b}^2-64{\mathit{\_}\mathit{C}\mathit{2}}^2{a}^{2}bc-16{\mathit{\_}\mathit{C}\mathit{2}}^2{a}^2{c}^2+32{\mathit{\_}\mathit{C}\mathit{2}}^{2}a{b}^{2}c+32{\mathit{\_}\mathit{C}\mathit{2}}^{2}ab{c}^2-16{\mathit{\_}\mathit{C}\mathit{2}}^2{b}^2{c}^2+\mathit{\_}\mathit{C}\mathit{1}bc)}}d\mathit{\_}\mathit{a}+t+\mathit{\_}\mathit{C}\mathit{3}),x\left(t\right)=\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-{\int }^{\mathit{\_}\mathit{Z}}2\frac{bc(a-c)(a-b)}{\sqrt{bc(a-c)(a-b)(-4a^4{\mathit{\_}\mathit{a}}^4+8{\mathit{\_}\mathit{a}}^4{a}^{3}b+8{\mathit{\_}\mathit{a}}^4{a}^{3}c-4{\mathit{\_}\mathit{a}}^4{a}^2{b}^2-16{\mathit{\_}\mathit{a}}^4{a}^{2}bc-4{\mathit{\_}\mathit{a}}^4{a}^2{c}^2+8{\mathit{\_}\mathit{a}}^{4}a{b}^{2}c+8{\mathit{\_}\mathit{a}}^{4}ab{c}^2-4{\mathit{\_}\mathit{a}}^4{b}^2{c}^2+16\mathit{\_}\mathit{C}\mathit{2}{\mathit{\_}\mathit{a}}^2{a}^4-32\mathit{\_}\mathit{C}\mathit{2}{\mathit{\_}\mathit{a}}^2{a}^{3}b-32\mathit{\_}\mathit{C}\mathit{2}{\mathit{\_}\mathit{a}}^2{a}^{3}c+16\mathit{\_}\mathit{C}\mathit{2}{\mathit{\_}\mathit{a}}^2{a}^2{b}^2+64\mathit{\_}\mathit{C}\mathit{2}{\mathit{\_}\mathit{a}}^2{a}^{2}bc+16\mathit{\_}\mathit{C}\mathit{2}{\mathit{\_}\mathit{a}}^2{a}^2{c}^2-32\mathit{\_}\mathit{C}\mathit{2}{\mathit{\_}\mathit{a}}^{2}a{b}^{2}c-32\mathit{\_}\mathit{C}\mathit{2}{\mathit{\_}\mathit{a}}^{2}ab{c}^2+16\mathit{\_}\mathit{C}\mathit{2}{\mathit{\_}\mathit{a}}^2{b}^2{c}^2-16{\mathit{\_}\mathit{C}\mathit{2}}^2{a}^4+32{\mathit{\_}\mathit{C}\mathit{2}}^2{a}^{3}b+32{\mathit{\_}\mathit{C}\mathit{2}}^2{a}^{3}c-16{\mathit{\_}\mathit{C}\mathit{2}}^2{a}^2{b}^2-64{\mathit{\_}\mathit{C}\mathit{2}}^2{a}^{2}bc-16{\mathit{\_}\mathit{C}\mathit{2}}^2{a}^2{c}^2+32{\mathit{\_}\mathit{C}\mathit{2}}^{2}a{b}^{2}c+32{\mathit{\_}\mathit{C}\mathit{2}}^{2}ab{c}^2-16{\mathit{\_}\mathit{C}\mathit{2}}^2{b}^2{c}^2+\mathit{\_}\mathit{C}\mathit{1}bc)}}d\mathit{\_}\mathit{a}+t+\mathit{\_}\mathit{C}\mathit{3})\},\{y\left(t\right)=-\frac{\sqrt{2}}{2bx\left(t\right)(b-c)(a-b)}\sqrt{x\left(t\right)b(b-c)(a-b)(bc\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}x\left(t\right)-\sqrt{4}\sqrt{c(\frac{bc{\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}x\left(t\right)\right)}^2}{4}+{\left(x\left(t\right)\right)}^2{\left(\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)\right)}^2(a-c)(a-b))b})a},y\left(t\right)=\frac{\sqrt{2}}{2bx\left(t\right)(b-c)(a-b)}\sqrt{x\left(t\right)b(b-c)(a-b)(bc\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}x\left(t\right)-\sqrt{4}\sqrt{c(\frac{bc{\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}x\left(t\right)\right)}^2}{4}+{\left(x\left(t\right)\right)}^2{\left(\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)\right)}^2(a-c)(a-b))b})a},y\left(t\right)=-\frac{\sqrt{2}}{2bx\left(t\right)(b-c)(a-b)}\sqrt{x\left(t\right)b(b-c)(a-b)(bc\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}x\left(t\right)+\sqrt{4}\sqrt{c(\frac{bc{\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}x\left(t\right)\right)}^2}{4}+{\left(x\left(t\right)\right)}^2{\left(\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)\right)}^2(a-c)(a-b))b})a},y\left(t\right)=\frac{\sqrt{2}}{2bx\left(t\right)(b-c)(a-b)}\sqrt{x\left(t\right)b(b-c)(a-b)(bc\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}x\left(t\right)+\sqrt{4}\sqrt{c(\frac{bc{\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}x\left(t\right)\right)}^2}{4}+{\left(x\left(t\right)\right)}^2{\left(\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)\right)}^2(a-c)(a-b))b})a}\},\{z\left(t\right)=\frac{a\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)}{y\left(t\right)(b-c)}\}]\}$$