Internal problem ID [365]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.6, Multiple Eigenvalue Solutions. Page 451
Problem number: problem 8.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=25 x_{1} \left (t \right )+12 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-18 x_{1} \left (t \right )-5 x_{2} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=6 x_{1} \left (t \right )+6 x_{2} \left (t \right )+13 x_{3} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 60
dsolve([diff(x__1(t),t)=25*x__1(t)+12*x__2(t)+0*x__3(t),diff(x__2(t),t)=-18*x__1(t)-5*x__2(t)+0*x__3(t),diff(x__3(t),t)=6*x__1(t)+6*x__2(t)+13*x__3(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= c_{2} {\mathrm e}^{7 t}+c_{3} {\mathrm e}^{13 t} \\ x_{2} \left (t \right ) &= -\frac {3 c_{2} {\mathrm e}^{7 t}}{2}-c_{3} {\mathrm e}^{13 t} \\ x_{3} \left (t \right ) &= \frac {c_{2} {\mathrm e}^{7 t}}{2}+\frac {c_{3} {\mathrm e}^{13 t}}{2}+{\mathrm e}^{13 t} c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 107
DSolve[{x1'[t]==25*x1[t]+12*x2[t]+0*x3[t],x2'[t]==-18*x1[t]-5*x2[t]+0*x3[t],x3'[t]==6*x1[t]+6*x2[t]+13*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{7 t} \left (c_1 \left (3 e^{6 t}-2\right )+2 c_2 \left (e^{6 t}-1\right )\right ) \\ \text {x2}(t)\to -e^{7 t} \left (3 c_1 \left (e^{6 t}-1\right )+c_2 \left (2 e^{6 t}-3\right )\right ) \\ \text {x3}(t)\to e^{7 t} \left (c_1 \left (e^{6 t}-1\right )+c_2 \left (e^{6 t}-1\right )+c_3 e^{6 t}\right ) \\ \end{align*}