Internal problem ID [9476]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1901.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=y \left (t \right )-z \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right )+y \left (t \right )\\ z^{\prime }\left (t \right )&=x \left (t \right )+z \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.453 (sec). Leaf size: 45
dsolve([diff(x(t),t)=y(t)-z(t),diff(y(t),t)=x(t)+y(t),diff(z(t),t)=x(t)+z(t)],[x(t), y(t), z(t)], singsol=all)
\[ x \left (t \right ) = c_{3} {\mathrm e}^{t}-c_{1} \] \[ y \left (t \right ) = c_{2} {\mathrm e}^{t}+c_{3} {\mathrm e}^{t}+c_{3} t \,{\mathrm e}^{t}+c_{1} \] \[ z \left (t \right ) = c_{1} +c_{2} {\mathrm e}^{t}+c_{3} t \,{\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 87
DSolve[{x'[t]==y[t]-z[t],y'[t]==x[t]+y[t],z'[t]==x[t]+z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to (c_2-c_3) \left (e^t-1\right )+c_1 \\ y(t)\to e^t ((c_2-c_3) t+c_1+c_3)-c_1+c_2-c_3 \\ z(t)\to e^t (c_2 (t-1)-c_3 (t-2)+c_1)-c_1+c_2-c_3 \\ \end{align*}