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 }\relax (t )&=139 x_{1} \relax (t )-14 x_{2} \relax (t )-52 x_{3} \relax (t )-14 x_{4} \relax (t )+28 x_{5} \relax (t )\\ x_{2}^{\prime }\relax (t )&=-22 x_{1} \relax (t )+5 x_{2} \relax (t )+7 x_{3} \relax (t )+8 x_{4} \relax (t )-7 x_{5} \relax (t )\\ x_{3}^{\prime }\relax (t )&=370 x_{1} \relax (t )-38 x_{2} \relax (t )-139 x_{3} \relax (t )-38 x_{4} \relax (t )+76 x_{5} \relax (t )\\ x_{4}^{\prime }\relax (t )&=152 x_{1} \relax (t )-16 x_{2} \relax (t )-59 x_{3} \relax (t )-13 x_{4} \relax (t )+35 x_{5} \relax (t )\\ x_{5}^{\prime }\relax (t )&=95 x_{1} \relax (t )-10 x_{2} \relax (t )-38 x_{3} \relax (t )-7 x_{4} \relax (t )+23 x_{5} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 130
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)],[x__1(t), x__2(t), x__3(t), x__4(t), x__5(t)], singsol=all)
\[ x_{1} \relax (t ) = c_{3} {\mathrm e}^{-3 t}+{\mathrm e}^{3 t} c_{4}+2 c_{5} {\mathrm e}^{9 t} \] \[ x_{2} \relax (t ) = c_{2} {\mathrm e}^{6 t}+7 \,{\mathrm e}^{3 t} c_{4}+3 c_{1} \] \[ x_{3} \relax (t ) = 3 c_{3} {\mathrm e}^{-3 t}+{\mathrm e}^{3 t} c_{4}+5 c_{5} {\mathrm e}^{9 t} \] \[ x_{4} \relax (t ) = c_{2} {\mathrm e}^{6 t}+c_{3} {\mathrm e}^{-3 t}+{\mathrm e}^{3 t} c_{4}+2 c_{5} {\mathrm e}^{9 t}-c_{1} \] \[ x_{5} \relax (t ) = c_{1}+c_{2} {\mathrm e}^{6 t}+c_{3} {\mathrm e}^{-3 t}+{\mathrm e}^{3 t} c_{4}+c_{5} {\mathrm e}^{9 t} \]
✓ Solution by Mathematica
Time used: 0.047 (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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