Internal problem ID [1824]
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: 1.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=6 x_{1} \relax (t )-3 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: 0.062 (sec). Leaf size: 35
dsolve([diff(x__1(t),t)=6*x__1(t)-3*x__2(t),diff(x__2(t),t)=2*x__1(t)+1*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \relax (t ) = \frac {3 c_{1} {\mathrm e}^{4 t}}{2}+c_{2} {\mathrm e}^{3 t} \] \[ x_{2} \relax (t ) = c_{1} {\mathrm e}^{4 t}+c_{2} {\mathrm e}^{3 t} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 60
DSolve[{x1'[t]==6*x1[t]-3*x2[t],x2'[t]==2*x1[t]+1*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{3 t} \left (c_1 \left (3 e^t-2\right )-3 c_2 \left (e^t-1\right )\right ) \\ \text {x2}(t)\to e^{3 t} \left (2 c_1 \left (e^t-1\right )+c_2 \left (3-2 e^t\right )\right ) \\ \end{align*}