60.10.20 problem 1933

Internal problem ID [11931]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 9, system of higher order odes
Problem number : 1933
Date solved : Tuesday, January 28, 2025 at 06:24:10 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )+\frac {d}{d t}y \left (t \right )&=x \left (t \right ) y \left (t \right )\\ \frac {d}{d t}y \left (t \right )+\frac {d}{d t}z \left (t \right )&=y \left (t \right ) z \left (t \right )\\ \frac {d}{d t}x \left (t \right )+\frac {d}{d t}z \left (t \right )&=x \left (t \right ) z \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 1.788 (sec). Leaf size: 4314

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)],singsol=all)
 

\begin{align*} \left [\left \{x \left (t \right ) &= \frac {2}{2 c_{2} -t}\right \}, \left \{y \left (t \right ) = \left (\int -\frac {x \left (t \right )^{2} {\mathrm e}^{-\int x \left (t \right )d t}}{2}d t +c_{1} \right ) {\mathrm e}^{\int x \left (t \right )d t}\right \}, \{z = x \left (t \right )\}\right ] \\ \left [\left \{x \left (t \right ) &= \frac {2}{2 c_{2} -t}\right \}, \{y \left (t \right ) = x \left (t \right )\}, \left \{z = \left (\int -\frac {x \left (t \right )^{2} {\mathrm e}^{-\int x \left (t \right )d t}}{2}d t +c_{1} \right ) {\mathrm e}^{\int x \left (t \right )d t}\right \}\right ] \\ \text {Expression too large to display} \\ \end{align*}

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{D[x[t],t]+D[y[t],t]==x[t]*y[t],D[y[t],t]+D[z[t],t]==y[t]*z[t],D[x[t],t]+D[z[t],t]==x[t]*z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
 

Not solved