Internal problem ID [353]
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 50.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=9 x_{1} \left (t \right )+13 x_{2} \left (t \right )-13 x_{6} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-14 x_{1} \left (t \right )+19 x_{2} \left (t \right )-10 x_{3} \left (t \right )-20 x_{4} \left (t \right )+10 x_{5} \left (t \right )+4 x_{6} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=-30 x_{1} \left (t \right )+12 x_{2} \left (t \right )-7 x_{3} \left (t \right )-30 x_{4} \left (t \right )+12 x_{5} \left (t \right )+18 x_{6} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=-12 x_{1} \left (t \right )+10 x_{2} \left (t \right )-10 x_{3} \left (t \right )-9 x_{4} \left (t \right )+10 x_{5} \left (t \right )+2 x_{6} \left (t \right )\\ x_{5}^{\prime }\left (t \right )&=6 x_{1} \left (t \right )+9 x_{2} \left (t \right )+6 x_{4} \left (t \right )+5 x_{5} \left (t \right )-15 x_{6} \left (t \right )\\ x_{6}^{\prime }\left (t \right )&=-14 x_{1} \left (t \right )+23 x_{2} \left (t \right )-10 x_{3} \left (t \right )-20 x_{4} \left (t \right )+10 x_{5} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 135
dsolve([diff(x__1(t),t)=9*x__1(t)+13*x__2(t)+0*x__3(t)+0*x__4(t)+0*x__5(t)-13*x__6(t),diff(x__2(t),t)=-14*x__1(t)+19*x__2(t)-10*x__3(t)-20*x__4(t)+10*x__5(t)+4*x__6(t),diff(x__3(t),t)=-30*x__1(t)+12*x__2(t)-7*x__3(t)-30*x__4(t)+12*x__5(t)+18*x__6(t),diff(x__4(t),t)=-12*x__1(t)+10*x__2(t)-10*x__3(t)-9*x__4(t)+10*x__5(t)+2*x__6(t),diff(x__5(t),t)=6*x__1(t)+9*x__2(t)+0*x__3(t)+6*x__4(t)+5*x__5(t)-15*x__6(t),diff(x__6(t),t)=-14*x__1(t)+23*x__2(t)-10*x__3(t)-20*x__4(t)+10*x__5(t)+0*x__6(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= c_{5} {\mathrm e}^{-4 t}+c_{6} {\mathrm e}^{9 t} \\ x_{2} \left (t \right ) &= c_{6} {\mathrm e}^{9 t}+c_{4} {\mathrm e}^{3 t}+{\mathrm e}^{-7 t} c_{3} \\ x_{3} \left (t \right ) &= {\mathrm e}^{-7 t} c_{3} -{\mathrm e}^{11 t} c_{2} +{\mathrm e}^{5 t} c_{1} \\ x_{4} \left (t \right ) &= {\mathrm e}^{11 t} c_{2} +c_{4} {\mathrm e}^{3 t}+{\mathrm e}^{-7 t} c_{3} \\ x_{5} \left (t \right ) &= {\mathrm e}^{11 t} c_{2} +{\mathrm e}^{5 t} c_{1} +c_{5} {\mathrm e}^{-4 t} \\ x_{6} \left (t \right ) &= c_{6} {\mathrm e}^{9 t}+c_{5} {\mathrm e}^{-4 t}+c_{4} {\mathrm e}^{3 t}+{\mathrm e}^{-7 t} c_{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.107 (sec). Leaf size: 1882
DSolve[{x1'[t]==9*x1[t]+13*x2[t]-13*x6[t],x2'[t]==-14*x1[t]+19*x2[t]-10*x3[t]-20*x4[t]+10*x5[t]+4*x6[t],x3'[t]==-30*x1[t]+12*x2[t]-7*x3[t]-30*x4[t]+12*x5[t]+18*x6[t],x4'[t]==-12*x1[t]+10*x2[t]-10*x3[t]-9*x4[t]+10*x5[t]+2*x6[t],x5'[t]==6*x1[t]+9*x2[t]+6*x4[t]+5*x5[t]-15*x6[t],x6'[t]==-14*x1[t]+23*x2[t]-10*x3[t]-20*x4[t]-10*x5[t]},{x1[t],x2[t],x3[t],x4[t],x5[t],x6[t]},t,IncludeSingularSolutions -> True]
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