Internal problem ID [5902]
Book: THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS.
K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section: Chapter 5. Systems of First Order Differential Equations. Section 5.11 Problems. Page
360
Problem number: Problem 5.6.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )+x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 35
dsolve([diff(x__1(t),t)=-2*x__1(t)+x__2(t),diff(x__2(t),t)=x__1(t)-2*x__2(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= c_{2} {\mathrm e}^{-t}+c_{1} {\mathrm e}^{-3 t} \\ x_{2} \left (t \right ) &= c_{2} {\mathrm e}^{-t}-c_{1} {\mathrm e}^{-3 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 68
DSolve[{x1'[t]==-2*x1[t]+x2[t],x2'[t]==x1[t]-2*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{2} e^{-3 t} \left (c_1 \left (e^{2 t}+1\right )+c_2 \left (e^{2 t}-1\right )\right ) \\ \text {x2}(t)\to \frac {1}{2} e^{-3 t} \left (c_1 \left (e^{2 t}-1\right )+c_2 \left (e^{2 t}+1\right )\right ) \\ \end{align*}