Internal problem ID [15547]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 3 (Systems of differential equations). Section 23.2 The method of undetermined
coefficients. Exercises page 239
Problem number: 824.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-x \left (t \right )-2 y \left (t \right )+2 \,{\mathrm e}^{-t}\\ y^{\prime }\left (t \right )&=-y \left (t \right )-z \left (t \right )+1\\ z^{\prime }\left (t \right )&=-z \left (t \right )+1 \end {align*}
With initial conditions \[ [x \left (0\right ) = 1, y \left (0\right ) = 1, z \left (0\right ) = 1] \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 20
dsolve([diff(x(t),t)+x(t)+2*y(t) = 2*exp(-t), diff(y(t),t)+y(t)+z(t) = 1, diff(z(t),t)+z(t) = 1, x(0) = 1, y(0) = 1, z(0) = 1], singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{-t} \\ y \left (t \right ) &= {\mathrm e}^{-t} \\ z \left (t \right ) &= 1 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 22
DSolve[{x'[t]+x[t]+2*y[t]==2*Exp[-t],y'[t]+y[t]+z[t]==1,z'[t]+z[t]==1},{x[0]==1,y[0]==1,z[0]==1},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-t} \\ y(t)\to e^{-t} \\ z(t)\to 1 \\ \end{align*}