Internal problem ID [5149]
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 }\relax (t )&=-2 x_{1}\relax (t )+x_{2}\relax (t )\\ x_{2}^{\prime }\relax (t )&=x_{1}\relax (t )-2 x_{2}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.052 (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)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = -c_{1} {\mathrm e}^{-3 t}+c_{2} {\mathrm e}^{-t} \] \[ x_{2}\relax (t ) = c_{1} {\mathrm e}^{-3 t}+c_{2} {\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 42
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 e^{-2 t} (c_1 \cosh (t)+c_2 \sinh (t)) \\ \text {x2}(t)\to e^{-2 t} (c_2 \cosh (t)+c_1 \sinh (t)) \\ \end{align*}