Internal problem ID [15532]
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 22. Integration of homogeneous
linear systems with constant coefficients. Eulers method. Exercises page 230
Problem number: 809.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 x \left (t \right )-y \left (t \right )+z \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right )+z \left (t \right )\\ z^{\prime }\left (t \right )&=y \left (t \right )-2 z \left (t \right )-3 x \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 0, y \left (0\right ) = 0, z \left (0\right ) = 1] \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 35
dsolve([diff(x(t),t) = 2*x(t)-y(t)+z(t), diff(y(t),t) = x(t)+z(t), diff(z(t),t) = y(t)-2*z(t)-3*x(t), x(0) = 0, y(0) = 0, z(0) = 1], singsol=all)
\begin{align*} x \left (t \right ) &= 1-{\mathrm e}^{-t} \\ y \left (t \right ) &= 1-{\mathrm e}^{-t} \\ z \left (t \right ) &= 2 \,{\mathrm e}^{-t}-1 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 38
DSolve[{x'[t]==2*x[t]-y[t]+z[t],y'[t]==x[t]+z[t],z'[t]==y[t]-2*z[t]-3*x[t]},{x[0]==0,y[0]==0,z[0]==1},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 1-e^{-t} \\ y(t)\to 1-e^{-t} \\ z(t)\to 2 e^{-t}-1 \\ \end{align*}