Internal problem ID [1828]
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: 5.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=-7 x_{1}\relax (t )+6 x_{3}\relax (t )\\ x_{2}^{\prime }\relax (t )&=5 x_{2}\relax (t )\\ x_{3}^{\prime }\relax (t )&=6 x_{1}\relax (t )+2 x_{3}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.049 (sec). Leaf size: 45
dsolve([diff(x__1(t),t)=-7*x__1(t)+0*x__2(t)+6*x__3(t),diff(x__2(t),t)=0*x__1(t)+5*x__2(t)+0*x__3(t),diff(x__3(t),t)=6*x__1(t)+0*x__2(t)+2*x__3(t)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1}\relax (t ) = -2 c_{2} {\mathrm e}^{-10 t}+\frac {c_{3} {\mathrm e}^{5 t}}{2} \] \[ x_{2}\relax (t ) = c_{1} {\mathrm e}^{5 t} \] \[ x_{3}\relax (t ) = c_{2} {\mathrm e}^{-10 t}+c_{3} {\mathrm e}^{5 t} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 152
DSolve[{x1'[t]==-7*x1[t]+0*x2[t]+6*x3[t],x2'[t]==0*x1[t]+5*x2[t]+0*x3[t],x3'[t]==6*x1[t]+0*x2[t]+2*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{5} e^{-10 t} \left ((c_1+2 c_2) e^{15 t}+4 c_1-2 c_2\right ) \\ \text {x3}(t)\to \frac {1}{5} e^{-10 t} \left (2 (c_1+2 c_2) e^{15 t}-2 c_1+c_2\right ) \\ \text {x2}(t)\to c_3 e^{5 t} \\ \text {x1}(t)\to \frac {1}{5} e^{-10 t} \left ((c_1+2 c_2) e^{15 t}+4 c_1-2 c_2\right ) \\ \text {x3}(t)\to \frac {1}{5} e^{-10 t} \left (2 (c_1+2 c_2) e^{15 t}-2 c_1+c_2\right ) \\ \text {x2}(t)\to 0 \\ \end{align*}