Internal problem ID [1827]
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: 4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=7 x_{1}\relax (t )-x_{2}\relax (t )+6 x_{3}\relax (t )\\ x_{2}^{\prime }\relax (t )&=-10 x_{1}\relax (t )+4 x_{2}\relax (t )-12 x_{3}\relax (t )\\ x_{3}^{\prime }\relax (t )&=-2 x_{1}\relax (t )+x_{2}\relax (t )-x_{3}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.061 (sec). Leaf size: 73
dsolve([diff(x__1(t),t)=7*x__1(t)-1*x__2(t)+6*x__3(t),diff(x__2(t),t)=-10*x__1(t)+4*x__2(t)-12*x__3(t),diff(x__3(t),t)=-2*x__1(t)+1*x__2(t)-1*x__3(t)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1}\relax (t ) = -c_{1} {\mathrm e}^{3 t}-c_{2} {\mathrm e}^{2 t}-\frac {3 c_{3} {\mathrm e}^{5 t}}{2} \] \[ x_{2}\relax (t ) = 2 c_{1} {\mathrm e}^{3 t}+c_{2} {\mathrm e}^{2 t}+3 c_{3} {\mathrm e}^{5 t} \] \[ x_{3}\relax (t ) = c_{1} {\mathrm e}^{3 t}+c_{2} {\mathrm e}^{2 t}+c_{3} {\mathrm e}^{5 t} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 137
DSolve[{x1'[t]==7*x1[t]-1*x2[t]+6*x3[t],x2'[t]==-10*x1[t]+4*x2[t]-12*x3[t],x3'[t]==-2*x1[t]+1*x2[t]-1*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{2 t} \left (3 (c_1+c_3) e^{3 t}-(4 c_1+c_2+3 c_3) e^t+2 c_1+c_2\right ) \\ \text {x2}(t)\to e^{2 t} \left (-6 (c_1+c_3) e^{3 t}+2 (4 c_1+c_2+3 c_3) e^t-2 c_1-c_2\right ) \\ \text {x3}(t)\to e^{2 t} \left (-2 (c_1+c_3) e^{3 t}+(4 c_1+c_2+3 c_3) e^t-2 c_1-c_2\right ) \\ \end{align*}