Internal problem ID [9481]
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 }\relax (t )&=y \relax (t )-z \relax (t )\\ y^{\prime }\relax (t )&=x \relax (t )+y \relax (t )+t\\ z^{\prime }\relax (t )&=x \relax (t )+z \relax (t )+t \end {align*}
✓ Solution by Maple
Time used: 0.187 (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},{x(t), y(t), z(t)}, singsol=all)
\[ x \relax (t ) = c_{2}+c_{3} {\mathrm e}^{t} \] \[ y \relax (t ) = c_{3} t \,{\mathrm e}^{t}+c_{1} {\mathrm e}^{t}-c_{2}-t -1 \] \[ z \relax (t ) = c_{3} t \,{\mathrm e}^{t}+c_{1} {\mathrm e}^{t}-c_{3} {\mathrm e}^{t}-c_{2}-t -1 \]
✓ Solution by Mathematica
Time used: 0.018 (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*}