Internal problem ID [352]
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 49.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=139 x_{1} \left (t \right )-14 x_{2} \left (t \right )-52 x_{3} \left (t \right )-14 x_{4} \left (t \right )+28 x_{5} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-22 x_{1} \left (t \right )+5 x_{2} \left (t \right )+7 x_{3} \left (t \right )+8 x_{4} \left (t \right )-7 x_{5} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=370 x_{1} \left (t \right )-38 x_{2} \left (t \right )-139 x_{3} \left (t \right )-38 x_{4} \left (t \right )+76 x_{5} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=152 x_{1} \left (t \right )-16 x_{2} \left (t \right )-59 x_{3} \left (t \right )-13 x_{4} \left (t \right )+35 x_{5} \left (t \right )\\ x_{5}^{\prime }\left (t \right )&=95 x_{1} \left (t \right )-10 x_{2} \left (t \right )-38 x_{3} \left (t \right )-7 x_{4} \left (t \right )+23 x_{5} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 132
dsolve([diff(x__1(t),t)=139*x__1(t)-14*x__2(t)-52*x__3(t)-14*x__4(t)+28*x__5(t),diff(x__2(t),t)=-22*x__1(t)+5*x__2(t)+7*x__3(t)+8*x__4(t)-7*x__5(t),diff(x__3(t),t)=370*x__1(t)-38*x__2(t)-139*x__3(t)-38*x__4(t)+76*x__5(t),diff(x__4(t),t)=152*x__1(t)-16*x__2(t)-59*x__3(t)-13*x__4(t)+35*x__5(t),diff(x__5(t),t)=95*x__1(t)-10*x__2(t)-38*x__3(t)-7*x__4(t)+23*x__5(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= c_{3} {\mathrm e}^{3 t}+c_{4} {\mathrm e}^{9 t}+c_{5} {\mathrm e}^{-3 t} \\ x_{2} \left (t \right ) &= \frac {{\mathrm e}^{6 t} c_{1}}{6}+7 c_{3} {\mathrm e}^{3 t}+c_{2} \\ x_{3} \left (t \right ) &= c_{3} {\mathrm e}^{3 t}+\frac {5 c_{4} {\mathrm e}^{9 t}}{2}+3 c_{5} {\mathrm e}^{-3 t} \\ x_{4} \left (t \right ) &= c_{3} {\mathrm e}^{3 t}+c_{4} {\mathrm e}^{9 t}+c_{5} {\mathrm e}^{-3 t}+\frac {{\mathrm e}^{6 t} c_{1}}{6}-\frac {c_{2}}{3} \\ x_{5} \left (t \right ) &= c_{3} {\mathrm e}^{3 t}+\frac {{\mathrm e}^{6 t} c_{1}}{6}+\frac {c_{4} {\mathrm e}^{9 t}}{2}+c_{5} {\mathrm e}^{-3 t}+\frac {c_{2}}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 2676
DSolve[{x1'[t]==139*x1[t]-14*x2[t]-52*x3[t]-14*x4[t]+28*x5[t],x2'[t]==-22*x1[t]+5*x2[t]+7*x3[t]+8*x4[t]-7*x5[t],x3'[t]==370*x1[t]-38*x2[t]-139*x3[t]-38*x4[t]+76*x5[t],x4'[t]==152*x1[t]-16*x2[t]-59*x3[t]-13*x4[t]+45*x5[t],x5'[t]==95*x1[t]-10*x2[t]-38*x3[t]-7*x4[t]+23*x5[t]},{x1[t],x2[t],x3[t],x4[t],x5[t]},t,IncludeSingularSolutions -> True]
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