10.17 problem 16

Internal problem ID [5990]

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

✓ Solution by Maple

Time used: 0.251 (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)],[x__1(t), x__2(t), x__3(t), x__4(t), x__5(t)], singsol=all)
 

\[ x_{1}\relax (t ) = -\frac {346378788000 \left (\moverset {5}{\munderset {\textit {\_a} =1}{\sum }}\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right )^{2} {\mathrm e}^{\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{2512446718921}+\frac {15248812500 \left (\moverset {5}{\munderset {\textit {\_a} =1}{\sum }}\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right )^{3} {\mathrm e}^{\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{2512446718921}-\frac {1155099105820 \left (\moverset {5}{\munderset {\textit {\_a} =1}{\sum }}\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right ) {\mathrm e}^{\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{2512446718921}-\frac {538124307820 \left (\moverset {5}{\munderset {\textit {\_a} =1}{\sum }}{\mathrm e}^{\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{2512446718921}+\frac {24122625000 \left (\moverset {5}{\munderset {\textit {\_a} =1}{\sum }}\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right )^{4} {\mathrm e}^{\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{2512446718921} \] \[ x_{2}\relax (t ) = -\frac {1216113967980 \left (\moverset {5}{\munderset {\textit {\_a} =1}{\sum }}\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right ) {\mathrm e}^{\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{2512446718921}+\frac {13519594578350 \left (\moverset {5}{\munderset {\textit {\_a} =1}{\sum }}{\mathrm e}^{\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{2512446718921}-\frac {6739842774000 \left (\moverset {5}{\munderset {\textit {\_a} =1}{\sum }}\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right )^{2} {\mathrm e}^{\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{2512446718921}-\frac {508009681000 \left (\moverset {5}{\munderset {\textit {\_a} =1}{\sum }}\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right )^{3} {\mathrm e}^{\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{2512446718921}+\frac {462980781000 \left (\moverset {5}{\munderset {\textit {\_a} =1}{\sum }}\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right )^{4} {\mathrm e}^{\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{2512446718921} \] \[ x_{3}\relax (t ) = -\frac {625855092300 \left (\moverset {5}{\munderset {\textit {\_a} =1}{\sum }}\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right ) {\mathrm e}^{\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{2512446718921}-\frac {1833221886500 \left (\moverset {5}{\munderset {\textit {\_a} =1}{\sum }}\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right )^{2} {\mathrm e}^{\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{2512446718921}+\frac {2847617760500 \left (\moverset {5}{\munderset {\textit {\_a} =1}{\sum }}{\mathrm e}^{\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{2512446718921}-\frac {47850114000 \left (\moverset {5}{\munderset {\textit {\_a} =1}{\sum }}\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right )^{3} {\mathrm e}^{\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{2512446718921}+\frac {109663110000 \left (\moverset {5}{\munderset {\textit {\_a} =1}{\sum }}\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right )^{4} {\mathrm e}^{\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{2512446718921} \] \[ x_{4}\relax (t ) = -\frac {481220518250 \left (\moverset {5}{\munderset {\textit {\_a} =1}{\sum }}\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right ) {\mathrm e}^{\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{2512446718921}+\frac {670465771350 \left (\moverset {5}{\munderset {\textit {\_a} =1}{\sum }}{\mathrm e}^{\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{2512446718921}-\frac {646573737600 \left (\moverset {5}{\munderset {\textit {\_a} =1}{\sum }}\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right )^{2} {\mathrm e}^{\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{2512446718921}+\frac {28464450000 \left (\moverset {5}{\munderset {\textit {\_a} =1}{\sum }}\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right )^{3} {\mathrm e}^{\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{2512446718921}+\frac {45028900000 \left (\moverset {5}{\munderset {\textit {\_a} =1}{\sum }}\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right )^{4} {\mathrm e}^{\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )}{2512446718921} \] \[ x_{5}\relax (t ) = \moverset {5}{\munderset {\textit {\_a} =1}{\sum }}{\mathrm e}^{\RootOf \left (500 \textit {\_Z}^{5}-3050 \textit {\_Z}^{4}-4450 \textit {\_Z}^{3}+35110 \textit {\_Z}^{2}+20779 \textit {\_Z} -81879, \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}} \]

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 2843

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]
 

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