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 }\left (t \right )&=-7 x_{1} \left (t \right )+6 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=5 x_{2} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=6 x_{1} \left (t \right )+2 x_{3} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (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)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= c_{1} {\mathrm e}^{-10 t}+c_{2} {\mathrm e}^{5 t} \\ x_{2} \left (t \right ) &= c_{3} {\mathrm e}^{5 t} \\ x_{3} \left (t \right ) &= -\frac {c_{1} {\mathrm e}^{-10 t}}{2}+2 c_{2} {\mathrm e}^{5 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 158
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 \left (e^{15 t}+4\right )+2 c_2 \left (e^{15 t}-1\right )\right ) \\ \text {x3}(t)\to \frac {1}{5} e^{-10 t} \left (2 c_1 \left (e^{15 t}-1\right )+c_2 \left (4 e^{15 t}+1\right )\right ) \\ \text {x2}(t)\to c_3 e^{5 t} \\ \text {x1}(t)\to \frac {1}{5} e^{-10 t} \left (c_1 \left (e^{15 t}+4\right )+2 c_2 \left (e^{15 t}-1\right )\right ) \\ \text {x3}(t)\to \frac {1}{5} e^{-10 t} \left (2 c_1 \left (e^{15 t}-1\right )+c_2 \left (4 e^{15 t}+1\right )\right ) \\ \text {x2}(t)\to 0 \\ \end{align*}