Internal problem ID [316]
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 2.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+3 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: 0.016 (sec). Leaf size: 36
dsolve([diff(x__1(t),t)=2*x__1(t)+3*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}^{4 t}+c_{2} {\mathrm e}^{-t} \\ x_{2} \left (t \right ) &= \frac {2 c_{1} {\mathrm e}^{4 t}}{3}-c_{2} {\mathrm e}^{-t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 74
DSolve[{x1'[t]==2*x1[t]+3*x2[t],x2'[t]==2*x1[t]+x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{5} e^{-t} \left (c_1 \left (3 e^{5 t}+2\right )+3 c_2 \left (e^{5 t}-1\right )\right ) \\ \text {x2}(t)\to \frac {1}{5} e^{-t} \left (2 c_1 \left (e^{5 t}-1\right )+c_2 \left (2 e^{5 t}+3\right )\right ) \\ \end{align*}