10.17 problem 16

Internal problem ID [6743]

Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section: CHAPTER 8 SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS. EXERCISES 8.2. Page 346
Problem number: 16.
ODE order: 1.
ODE degree: 1.

Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )+2 x_{3} \left (t \right )-\frac {9 x_{4} \left (t \right )}{5}\\ x_{2}^{\prime }\left (t \right )&=\frac {51 x_{2} \left (t \right )}{10}-x_{4} \left (t \right )+3 x_{5} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=x_{2} \left (t \right )-\frac {31 x_{3} \left (t \right )}{10}+4 x_{4} \left (t \right )\\ x_{5}^{\prime }\left (t \right )&=-\frac {14 x_{1} \left (t \right )}{5}+\frac {3 x_{4} \left (t \right )}{2}-x_{5} \left (t \right ) \end {align*}

✓ Solution by Maple

Time used: 0.094 (sec). Leaf size: 1389

dsolve([diff(x__1(t),t)=x__1(t)+2*x__3(t)-18/10*x__4(t),diff(x__2(t),t)=51/10*x__2(t)-x__4(t)+3*x__5(t),diff(x__3(t),t)=x__1(t)+2*x__2(t)-3*x__3(t),diff(x__4(t),t)=x__2(t)-31/10*x__3(t)+4*x__4(t),diff(x__5(t),t)=-28/10*x__1(t)+15/10*x__4(t)-x__5(t)],singsol=all)
 

\begin{align*} x_{1} \left (t \right ) &= \frac {1334393 \left (\moverset {5}{\munderset {\textit {\_a} &=1}{\sum }}\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right ) {\mathrm e}^{\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{1052220}+\frac {3565 \left (\moverset {5}{\munderset {\textit {\_a} &=1}{\sum }}\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right )^{4} {\mathrm e}^{\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{105222}-\frac {29663 \left (\moverset {5}{\munderset {\textit {\_a} &=1}{\sum }}\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right )^{3} {\mathrm e}^{\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{210444}-\frac {49145 \left (\moverset {5}{\munderset {\textit {\_a} &=1}{\sum }}\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right )^{2} {\mathrm e}^{\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{105222}+\frac {20174057 \left (\moverset {5}{\munderset {\textit {\_a} &=1}{\sum }}{\mathrm e}^{\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{10522200} \\ x_{2} \left (t \right ) &= -\frac {16027 \left (\moverset {5}{\munderset {\textit {\_a} &=1}{\sum }}\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right )^{3} {\mathrm e}^{\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{420888}+\frac {10385 \left (\moverset {5}{\munderset {\textit {\_a} &=1}{\sum }}\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right )^{4} {\mathrm e}^{\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{210444}-\frac {210025 \left (\moverset {5}{\munderset {\textit {\_a} &=1}{\sum }}\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right )^{2} {\mathrm e}^{\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{210444}-\frac {371003 \left (\moverset {5}{\munderset {\textit {\_a} &=1}{\sum }}\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right ) {\mathrm e}^{\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{2104440}+\frac {92973853 \left (\moverset {5}{\munderset {\textit {\_a} &=1}{\sum }}{\mathrm e}^{\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{21044400} \\ x_{3} \left (t \right ) &= -\frac {33875 \left (\moverset {5}{\munderset {\textit {\_a} &=1}{\sum }}\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right )^{2} {\mathrm e}^{\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{105222}-\frac {2585 \left (\moverset {5}{\munderset {\textit {\_a} &=1}{\sum }}\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right )^{3} {\mathrm e}^{\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{210444}-\frac {79853 \left (\moverset {5}{\munderset {\textit {\_a} &=1}{\sum }}\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right ) {\mathrm e}^{\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{210444}+\frac {1675 \left (\moverset {5}{\munderset {\textit {\_a} &=1}{\sum }}\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right )^{4} {\mathrm e}^{\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{105222}+\frac {5714563 \left (\moverset {5}{\munderset {\textit {\_a} &=1}{\sum }}{\mathrm e}^{\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{2104440} \\ x_{4} \left (t \right ) &= \moverset {5}{\munderset {\textit {\_a} &=1}{\sum }}{\mathrm e}^{\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}} \\ x_{5} \left (t \right ) &= \frac {527 \left (\moverset {5}{\munderset {\textit {\_a} &=1}{\sum }}\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right )^{4} {\mathrm e}^{\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{140296}-\frac {511531 \left (\moverset {5}{\munderset {\textit {\_a} &=1}{\sum }}\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right )^{3} {\mathrm e}^{\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{4208880}+\frac {203195 \left (\moverset {5}{\munderset {\textit {\_a} &=1}{\sum }}\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right )^{2} {\mathrm e}^{\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{420888}+\frac {7637447 \left (\moverset {5}{\munderset {\textit {\_a} &=1}{\sum }}\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right ) {\mathrm e}^{\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{7014800}-\frac {943531891 \left (\moverset {5}{\munderset {\textit {\_a} &=1}{\sum }}{\mathrm e}^{\operatorname {RootOf}\left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \operatorname {index} &=\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{210444000} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 2839

DSolve[{x1'[t]==x1[t]+2*x3[t]-18/10*x4[t],x2'[t]==51/10*x2[t]-x4[t]+3*x5[t],x3'[t]==x1[t]+2*x2[t]-3*x3[t],x4'[t]==x2[t]-31/10*x3[t]+4*x4[t],x5'[t]==-28/10*x1[t]+15/10*x4[t]-x5[t]},{x1[t],x2[t],x3[t],x4[t],x5[t]},t,IncludeSingularSolutions -> True]
 

Too large to display