2.1911   ODE No. 1911

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

$$\{at{x}^{\prime }(t)=bc(y(t)-z(t)),bt{y}^{\prime }(t)=ac(z(t)-x(t)),ct{z}^{\prime }(t)=ab(x(t)-y(t))\}$$ ✗ Mathematica : cpu = 0.0310907 (sec), leaf count = 0 , could not solve

DSolve[{a*t*Derivative[1][x][t] == b*c*(y[t] - z[t]), b*t*Derivative[1][y][t] == a*c*(-x[t] + z[t]), c*t*Derivative[1][z][t] == a*b*(x[t] - y[t])}, {x[t], y[t], z[t]}, t]

✓ Maple : cpu = 0.159 (sec), leaf count = 308

$$\left\{\{x\left(t\right)=\mathit{\_}\mathit{C}\mathit{1}+\mathit{\_}\mathit{C}\mathit{2}\sin (\sqrt{a^2+b^2+c^2}\ln \left(t\right))+\mathit{\_}\mathit{C}\mathit{3}\cos (\sqrt{a^2+b^2+c^2}\ln \left(t\right)),y\left(t\right)=\frac{1}{b(b^2+c^2)}(\sqrt{a^2+b^2+c^2}\cos (\sqrt{a^2+b^2+c^2}\ln \left(t\right))\mathit{\_}\mathit{C}\mathit{2}ac-\sqrt{a^2+b^2+c^2}\sin (\sqrt{a^2+b^2+c^2}\ln \left(t\right))\mathit{\_}\mathit{C}\mathit{3}ac-\cos (\sqrt{a^2+b^2+c^2}\ln \left(t\right))\mathit{\_}\mathit{C}\mathit{3}{a}^{2}b-\sin (\sqrt{a^2+b^2+c^2}\ln \left(t\right))\mathit{\_}\mathit{C}\mathit{2}{a}^{2}b+\mathit{\_}\mathit{C}\mathit{1}{b}^3+\mathit{\_}\mathit{C}\mathit{1}b{c}^2),z\left(t\right)=\frac{1}{(b^2+c^2)c}(\mathit{\_}\mathit{C}\mathit{1}{c}^3+((-\mathit{\_}\mathit{C}\mathit{2}\sin (\sqrt{a^2+b^2+c^2}\ln \left(t\right))-\mathit{\_}\mathit{C}\mathit{3}\cos (\sqrt{a^2+b^2+c^2}\ln \left(t\right)))a^2+\mathit{\_}\mathit{C}\mathit{1}{b}^2)c+ba\sqrt{a^2+b^2+c^2}(\sin (\sqrt{a^2+b^2+c^2}\ln \left(t\right))\mathit{\_}\mathit{C}\mathit{3}-\cos (\sqrt{a^2+b^2+c^2}\ln \left(t\right))\mathit{\_}\mathit{C}\mathit{2}))\}\right\}$$