Internal problem ID [1825]
Book: Differential equations and their applications, 4th ed., M. Braun
Section: Section 3.8, Systems of differential equations. The eigenva1ue-eigenvector method. Page
339
Problem number: 2.
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 )&=-4 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve([diff(x__1(t),t)=-2*x__1(t)+1*x__2(t),diff(x__2(t),t)=-4*x__1(t)+3*x__2(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{-t} c_{1} +c_{2} {\mathrm e}^{2 t} \\ x_{2} \left (t \right ) &= {\mathrm e}^{-t} c_{1} +4 c_{2} {\mathrm e}^{2 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 72
DSolve[{x1'[t]==-2*x1[t]+1*x2[t],x2'[t]==-4*x1[t]+3*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{3} e^{-t} \left (c_2 \left (e^{3 t}-1\right )-c_1 \left (e^{3 t}-4\right )\right ) \\ \text {x2}(t)\to \frac {1}{3} e^{-t} \left (c_2 \left (4 e^{3 t}-1\right )-4 c_1 \left (e^{3 t}-1\right )\right ) \\ \end{align*}