Internal problem ID [10225]
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: 0.032 (sec). Leaf size: 56
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],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} +c_{3} {\mathrm e}^{t} \\ y \left (t \right ) &= c_{3} {\mathrm e}^{t} t +c_{1} {\mathrm e}^{t}-c_{2} -t -1 \\ z \left (t \right ) &= c_{3} {\mathrm e}^{t} t +c_{1} {\mathrm e}^{t}-c_{3} {\mathrm e}^{t}-c_{2} -t -1 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 109
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 c_1 \left (e^t-1\right )+t \left (-1+(c_2-c_3) e^t\right )+c_3 e^t-1+c_2-c_3 \\ z(t)\to c_1 \left (e^t-1\right )-c_2 e^t+t \left (-1+(c_2-c_3) e^t\right )+2 c_3 e^t-1+c_2-c_3 \\ \end{align*}