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 }\relax (t )&=y \relax (t )+z \relax (t )\\ y^{\prime }\relax (t )&=z \relax (t )+x \relax (t )\\ z^{\prime }\relax (t )&=x \relax (t )+y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.11 (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)],[x(t), y(t), z(t)], singsol=all)
\[ x \relax (t ) = -2 c_{2} {\mathrm e}^{-t}+c_{3} {\mathrm e}^{2 t}-{\mathrm e}^{-t} c_{1} \] \[ y \relax (t ) = c_{2} {\mathrm e}^{-t}+c_{3} {\mathrm e}^{2 t}+{\mathrm e}^{-t} c_{1} \] \[ z \relax (t ) = c_{2} {\mathrm e}^{-t}+c_{3} {\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 114
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+c_2+c_3) e^{3 t}-c_1+2 c_2-c_3\right ) \\ z(t)\to \frac {1}{3} e^{-t} \left ((c_1+c_2+c_3) e^{3 t}-c_1-c_2+2 c_3\right ) \\ \end{align*}