Internal problem ID [9512]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 9, system of higher order odes
Problem number: 1933.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )+y^{\prime }\relax (t )&=x \relax (t ) y \relax (t )\\ x^{\prime }\relax (t )+z^{\prime }\relax (t )&=x \relax (t ) z \relax (t )\\ y^{\prime }\relax (t )+z^{\prime }\relax (t )&=y \relax (t ) z \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 1.187 (sec). Leaf size: 4269
dsolve({diff(x(t),t)+diff(y(t),t)=x(t)*y(t),diff(y(t),t)+diff(z(t),t)=y(t)*z(t),diff(x(t),t)+diff(z(t),t)=x(t)*z(t)},{x(t), y(t), z(t)}, singsol=all)
\begin{align*} \left \{x \relax (t ) = \frac {2}{2 c_{2}-t}\right \} \\ \left \{y \relax (t ) = \left (\int -\frac {x \relax (t )^{2} {\mathrm e}^{-\left (\int x \relax (t )d t \right )}}{2}d t +c_{1}\right ) {\mathrm e}^{\int x \relax (t )d t}\right \} \\ \{z \relax (t ) = x \relax (t )\} \\ \end{align*} \begin{align*} \left \{x \relax (t ) = \frac {2}{2 c_{2}-t}\right \} \\ \{y \relax (t ) = x \relax (t )\} \\ \left \{z \relax (t ) = \left (\int -\frac {x \relax (t )^{2} {\mathrm e}^{-\left (\int x \relax (t )d t \right )}}{2}d t +c_{1}\right ) {\mathrm e}^{\int x \relax (t )d t}\right \} \\ \end{align*} \begin{align*} \text {Expression too large to display} \\ \left \{y \relax (t ) = -\frac {x \relax (t ) \left (\frac {d}{d t}x \relax (t )\right )-\frac {d^{2}}{d t^{2}}x \relax (t )-\sqrt {-3 \left (\frac {d}{d t}x \relax (t )\right )^{2} x \relax (t )^{2}+2 \left (\frac {d^{2}}{d t^{2}}x \relax (t )\right ) x \relax (t )^{3}+8 \left (\frac {d}{d t}x \relax (t )\right )^{3}-6 \left (\frac {d^{2}}{d t^{2}}x \relax (t )\right ) \left (\frac {d}{d t}x \relax (t )\right ) x \relax (t )+\left (\frac {d^{2}}{d t^{2}}x \relax (t )\right )^{2}}}{-x \relax (t )^{2}+2 \frac {d}{d t}x \relax (t )}, y \relax (t ) = -\frac {x \relax (t ) \left (\frac {d}{d t}x \relax (t )\right )-\frac {d^{2}}{d t^{2}}x \relax (t )+\sqrt {-3 \left (\frac {d}{d t}x \relax (t )\right )^{2} x \relax (t )^{2}+2 \left (\frac {d^{2}}{d t^{2}}x \relax (t )\right ) x \relax (t )^{3}+8 \left (\frac {d}{d t}x \relax (t )\right )^{3}-6 \left (\frac {d^{2}}{d t^{2}}x \relax (t )\right ) \left (\frac {d}{d t}x \relax (t )\right ) x \relax (t )+\left (\frac {d^{2}}{d t^{2}}x \relax (t )\right )^{2}}}{-x \relax (t )^{2}+2 \frac {d}{d t}x \relax (t )}\right \} \\ \left \{z \relax (t ) = \frac {-y \relax (t ) x \relax (t )+2 \frac {d}{d t}x \relax (t )}{x \relax (t )-y \relax (t )}\right \} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{x'[t]+y'[t]==x[t]*y[t],y'[t]+z'[t]==y[t]*z[t],x'[t]+z'[t]==x[t]*z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
Not solved