Internal problem ID [1826]
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: 3.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=3 x_{1} \relax (t )+2 x_{2} \relax (t )+4 x_{3} \relax (t )\\ x_{2}^{\prime }\relax (t )&=2 x_{1} \relax (t )+2 x_{3} \relax (t )\\ x_{3}^{\prime }\relax (t )&=4 x_{1} \relax (t )+2 x_{2} \relax (t )+3 x_{3} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 66
dsolve([diff(x__1(t),t)=3*x__1(t)+2*x__2(t)+4*x__3(t),diff(x__2(t),t)=2*x__1(t)+0*x__2(t)+2*x__3(t),diff(x__3(t),t)=4*x__1(t)+2*x__2(t)+3*x__3(t)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1} \relax (t ) = -\frac {5 c_{2} {\mathrm e}^{-t}}{4}+c_{3} {\mathrm e}^{8 t}-\frac {{\mathrm e}^{-t} c_{1}}{2} \] \[ x_{2} \relax (t ) = \frac {c_{2} {\mathrm e}^{-t}}{2}+\frac {c_{3} {\mathrm e}^{8 t}}{2}+{\mathrm e}^{-t} c_{1} \] \[ x_{3} \relax (t ) = c_{2} {\mathrm e}^{-t}+c_{3} {\mathrm e}^{8 t} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 127
DSolve[{x1'[t]==3*x1[t]+2*x2[t]+4*x3[t],x2'[t]==2*x1[t]+0*x2[t]+2*x3[t],x3'[t]==4*x1[t]+2*x2[t]+3*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{9} e^{-t} \left (c_1 \left (4 e^{9 t}+5\right )+2 (c_2+2 c_3) \left (e^{9 t}-1\right )\right ) \\ \text {x2}(t)\to \frac {1}{9} e^{-t} \left ((2 c_1+c_2+2 c_3) e^{9 t}-2 (c_1-4 c_2+c_3)\right ) \\ \text {x3}(t)\to \frac {1}{9} e^{-t} \left (2 (2 c_1+c_2+2 c_3) e^{9 t}-4 c_1-2 c_2+5 c_3\right ) \\ \end{align*}