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 }\relax (t )&=-2 x_{1}\relax (t )+x_{2}\relax (t )\\ x_{2}^{\prime }\relax (t )&=-4 x_{1}\relax (t )+3 x_{2}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.365 (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)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = {\mathrm e}^{-t} c_{1}+\frac {c_{2} {\mathrm e}^{2 t}}{4} \] \[ x_{2}\relax (t ) = {\mathrm e}^{-t} c_{1}+c_{2} {\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 71
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-c_1) e^{3 t}+4 c_1-c_2\right ) \\ \text {x2}(t)\to \frac {1}{3} e^{-t} \left (-4 (c_1-c_2) e^{3 t}+4 c_1-c_2\right ) \\ \end{align*}