9.4.38 problem problem 49

Internal problem ID [1002]
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
Date solved : Monday, January 27, 2025 at 03:22:50 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \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 )\\ \frac {d}{d t}x_{2} \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 )\\ \frac {d}{d t}x_{3} \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 )\\ \frac {d}{d t}x_{4} \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 )\\ \frac {d}{d t}x_{5} \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: 0.117 (sec). Leaf size: 131

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}^{3 t}+c_5 \,{\mathrm e}^{9 t} \\ x_{2} \left (t \right ) &= \frac {c_1 \,{\mathrm e}^{6 t}}{6}+7 c_4 \,{\mathrm e}^{3 t}+c_2 \\ x_{3} \left (t \right ) &= 3 c_3 \,{\mathrm e}^{-3 t}+c_4 \,{\mathrm e}^{3 t}+\frac {5 c_5 \,{\mathrm e}^{9 t}}{2} \\ x_{4} \left (t \right ) &= c_3 \,{\mathrm e}^{-3 t}+c_4 \,{\mathrm e}^{3 t}+c_5 \,{\mathrm e}^{9 t}+\frac {c_1 \,{\mathrm e}^{6 t}}{6}-\frac {c_2}{3} \\ x_{5} \left (t \right ) &= c_4 \,{\mathrm e}^{3 t}+\frac {c_1 \,{\mathrm e}^{6 t}}{6}+c_3 \,{\mathrm e}^{-3 t}+\frac {c_5 \,{\mathrm e}^{9 t}}{2}+\frac {c_2}{3} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 2676

DSolve[{D[ x1[t],t]==139*x1[t]-14*x2[t]-52*x3[t]-14*x4[t]+28*x5[t],D[ x2[t],t]==-22*x1[t]+5*x2[t]+7*x3[t]+8*x4[t]-7*x5[t],D[ x3[t],t]==370*x1[t]-38*x2[t]-139*x3[t]-38*x4[t]+76*x5[t],D[ x4[t],t]==152*x1[t]-16*x2[t]-59*x3[t]-13*x4[t]+45*x5[t],D[ x5[t],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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