Internal problem ID [805]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 9.1, The Phase Plane: Linear Systems. page 505
Problem number: 14.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=-2 x_{1}\relax (t )+x_{2}\relax (t )-2\\ x_{2}^{\prime }\relax (t )&=x_{1}\relax (t )-2 x_{2}\relax (t )+1 \end {align*}
✓ Solution by Maple
Time used: 0.021 (sec). Leaf size: 36
dsolve([diff(x__1(t),t)=-2*x__1(t)+1*x__2(t)-2,diff(x__2(t),t)=1*x__1(t)-2*x__2(t)+1],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = {\mathrm e}^{-t} c_{1}-c_{2} {\mathrm e}^{-3 t}-1 \] \[ x_{2}\relax (t ) = {\mathrm e}^{-t} c_{1}+c_{2} {\mathrm e}^{-3 t} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 57
DSolve[{x1'[t]==-2*x1[t]+1*x2[t]-2,x2'[t]==1*x1[t]-2*x2[t]+1},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{2} e^{-3 t} \left (e^{2 t} \left (-2 e^t+c_1+c_2\right )+c_1-c_2\right ) \\ \text {x2}(t)\to e^{-2 t} (c_2 \cosh (t)+c_1 \sinh (t)) \\ \end{align*}