Internal problem ID [275]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 7.2, Matrices and Linear systems. Page 417
Problem number: problem 7.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=y \left (t \right )+z \left (t \right )\\ y^{\prime }\left (t \right )&=z \left (t \right )+x\\ z^{\prime }\left (t \right )&=x+y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 64
dsolve([diff(x(t),t)=y(t)+z(t),diff(y(t),t)=z(t)+x(t),diff(z(t),t)=x(t)+y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{-t}+c_{3} {\mathrm e}^{2 t} \\ y \left (t \right ) &= c_{2} {\mathrm e}^{-t}+c_{3} {\mathrm e}^{2 t}+{\mathrm e}^{-t} c_{1} \\ z \left (t \right ) &= -2 c_{2} {\mathrm e}^{-t}+c_{3} {\mathrm e}^{2 t}-{\mathrm e}^{-t} c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 124
DSolve[{x'[t]==y[t]+z[t],y'[t]==z[t]+x[t],z'[t]==x[t]+y[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{3} e^{-t} \left (c_1 \left (e^{3 t}+2\right )+(c_2+c_3) \left (e^{3 t}-1\right )\right ) \\ y(t)\to \frac {1}{3} e^{-t} \left (c_1 \left (e^{3 t}-1\right )+c_2 \left (e^{3 t}+2\right )+c_3 \left (e^{3 t}-1\right )\right ) \\ z(t)\to \frac {1}{3} e^{-t} \left (c_1 \left (e^{3 t}-1\right )+c_2 \left (e^{3 t}-1\right )+c_3 \left (e^{3 t}+2\right )\right ) \\ \end{align*}