Internal problem ID [345]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.3, The eigenvalue method for linear systems. Page 395
Problem number: problem 42.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=-40 x_{1} \left (t \right )-12 x_{2} \left (t \right )+54 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=35 x_{1} \left (t \right )+13 x_{2} \left (t \right )-46 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=-25 x_{1} \left (t \right )-7 x_{2} \left (t \right )+34 x_{3} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 59
dsolve([diff(x__1(t),t)=-40*x__1(t)-12*x__2(t)+54*x__3(t),diff(x__2(t),t)=35*x__1(t)+13*x__2(t)-46*x__3(t),diff(x__3(t),t)=-25*x__1(t)-7*x__2(t)+34*x__3(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= c_{1} +c_{2} {\mathrm e}^{2 t}+c_{3} {\mathrm e}^{5 t} \\ x_{2} \left (t \right ) &= c_{2} {\mathrm e}^{2 t}-\frac {3 c_{3} {\mathrm e}^{5 t}}{2}-\frac {c_{1}}{3} \\ x_{3} \left (t \right ) &= c_{2} {\mathrm e}^{2 t}+\frac {c_{3} {\mathrm e}^{5 t}}{2}+\frac {2 c_{1}}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 181
DSolve[{x1'[t]==-40*x1[t]-12*x2[t]+54*x3[t],x2'[t]==35*x1[t]+13*x2[t]-46*x3[t],x3'[t]==-25*x1[t]-7*x2[t]+34*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to c_1 \left (-5 e^{2 t}-6 e^{5 t}+12\right )-c_2 \left (e^{2 t}+2 e^{5 t}-3\right )+c_3 \left (7 e^{2 t}+8 e^{5 t}-15\right ) \\ \text {x2}(t)\to c_1 \left (-5 e^{2 t}+9 e^{5 t}-4\right )+c_2 \left (-e^{2 t}+3 e^{5 t}-1\right )+c_3 \left (7 e^{2 t}-12 e^{5 t}+5\right ) \\ \text {x3}(t)\to c_1 \left (-5 e^{2 t}-3 e^{5 t}+8\right )-c_2 \left (e^{2 t}+e^{5 t}-2\right )+c_3 \left (7 e^{2 t}+4 e^{5 t}-10\right ) \\ \end{align*}