Internal problem ID [9477]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1902.
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 )+t\\ z^{\prime }\left (t \right )&=x \left (t \right )+z \left (t \right )+t \end {align*}
✓ Solution by Maple
Time used: 13.281 (sec). Leaf size: 49
dsolve([diff(x(t),t)-y(t)+z(t)=0,diff(y(t),t)-x(t)-y(t)=t,diff(z(t),t)-x(t)-z(t)=t],[x(t), y(t), z(t)], singsol=all)
\[ x \left (t \right ) = c_{1} {\mathrm e}^{t}-1-c_{3} \] \[ y \left (t \right ) = {\mathrm e}^{t} c_{1} t +c_{2} {\mathrm e}^{t}+c_{3} -t \] \[ z \left (t \right ) = \left (c_{2} +\left (t -1\right ) c_{1} \right ) {\mathrm e}^{t}+c_{3} -t \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 95
DSolve[{x'[t]-y[t]+z[t]==0,y'[t]-x[t]-y[t]==t,z'[t]-x[t]-z[t]==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 -t+e^t ((c_2-c_3) t+c_1+c_3)-1-c_1+c_2-c_3 \\ z(t)\to -t+e^t (c_2 (t-1)-c_3 (t-2)+c_1)-1-c_1+c_2-c_3 \\ \end{align*}