Internal problem ID [315]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.3, The eigenvalue method for linear systems. Page 395
Problem number: problem 1.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )+2 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve([diff(x__1(t),t)=x__1(t)+2*x__2(t),diff(x__2(t),t)=2*x__1(t)+x__2(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= c_{1} {\mathrm e}^{3 t}+c_{2} {\mathrm e}^{-t} \\ x_{2} \left (t \right ) &= c_{1} {\mathrm e}^{3 t}-c_{2} {\mathrm e}^{-t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 68
DSolve[{x1'[t]==x1[t]+2*x2[t],x2'[t]==2*x1[t]+x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{2} e^{-t} \left (c_1 \left (e^{4 t}+1\right )+c_2 \left (e^{4 t}-1\right )\right ) \\ \text {x2}(t)\to \frac {1}{2} e^{-t} \left (c_1 \left (e^{4 t}-1\right )+c_2 \left (e^{4 t}+1\right )\right ) \\ \end{align*}