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 }\relax (t )&=x_{1} \relax (t )+2 x_{2} \relax (t )\\ x_{2}^{\prime }\relax (t )&=2 x_{1} \relax (t )+x_{2} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.047 (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)],[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: 46
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 e^t (c_1 \cosh (2 t)+c_2 \sinh (2 t)) \\ \text {x2}(t)\to e^t (c_2 \cosh (2 t)+c_1 \sinh (2 t)) \\ \end{align*}