Internal problem ID [804]
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: 13.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )-2\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )-x_{2} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 70
dsolve([diff(x__1(t),t)=1*x__1(t)+1*x__2(t)-2,diff(x__2(t),t)=1*x__1(t)-1*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \left (t \right ) = \sqrt {2}\, {\mathrm e}^{t \sqrt {2}} c_{2} -\sqrt {2}\, {\mathrm e}^{-t \sqrt {2}} c_{1} +{\mathrm e}^{t \sqrt {2}} c_{2} +{\mathrm e}^{-t \sqrt {2}} c_{1} +1 \] \[ x_{2} \left (t \right ) = {\mathrm e}^{t \sqrt {2}} c_{2} +{\mathrm e}^{-t \sqrt {2}} c_{1} +1 \]
✓ Solution by Mathematica
Time used: 0.097 (sec). Leaf size: 160
DSolve[{x1'[t]==1*x1[t]+1*x2[t]-2,x2'[t]==1*x1[t]-1*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{4} e^{-\sqrt {2} t} \left (4 e^{\sqrt {2} t}+\left (\left (2+\sqrt {2}\right ) c_1+\sqrt {2} c_2\right ) e^{2 \sqrt {2} t}-\left (\left (\sqrt {2}-2\right ) c_1\right )-\sqrt {2} c_2\right ) \text {x2}(t)\to \frac {1}{4} e^{-\sqrt {2} t} \left (4 e^{\sqrt {2} t}+\left (\sqrt {2} c_1-\left (\sqrt {2}-2\right ) c_2\right ) e^{2 \sqrt {2} t}-\sqrt {2} c_1+\left (2+\sqrt {2}\right ) c_2\right ) \end{align*}