Internal problem ID [12747]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 3. Linear Systems. Exercises section 3.1. page 258
Problem number: 7.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} p^{\prime }\left (t \right )&=3 p \left (t \right )-2 q \left (t \right )-7 r \left (t \right )\\ q^{\prime }\left (t \right )&=-2 p \left (t \right )+6 r \left (t \right )\\ r^{\prime }\left (t \right )&=\frac {73 q \left (t \right )}{100}+2 r \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 910
dsolve([diff(p(t),t)=3*p(t)-2*q(t)-7*r(t),diff(q(t),t)=-2*p(t)+6*r(t),diff(r(t),t)=73/100*q(t)+2*r(t)],[p(t), q(t), r(t)], singsol=all)
\begin{align*} p \left (t \right ) = -\frac {\left (i \sqrt {3}\, \left (31130+6 i \sqrt {895302429}\right )^{\frac {4}{3}}-\left (31130+6 i \sqrt {895302429}\right )^{\frac {4}{3}}+128560 i \sqrt {3}\, \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}-11574996 i \sqrt {3}+3972 \left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}-240 i \sqrt {895302429}+720 \sqrt {298434143}-128560 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}-11574996\right ) c_{1} {\mathrm e}^{-\frac {\left (i \sqrt {3}\, \left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}-3214 i \sqrt {3}+\left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}-100 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}+3214\right ) t}{60 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}}}}{2628 \left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}}+\frac {\left (i \sqrt {3}\, \left (31130+6 i \sqrt {895302429}\right )^{\frac {4}{3}}+\left (31130+6 i \sqrt {895302429}\right )^{\frac {4}{3}}+128560 i \sqrt {3}\, \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}-11574996 i \sqrt {3}-3972 \left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}+240 i \sqrt {895302429}+720 \sqrt {298434143}+128560 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}+11574996\right ) c_{2} {\mathrm e}^{\frac {\left (i \sqrt {3}\, \left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}-3214 i \sqrt {3}-\left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}+100 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}-3214\right ) t}{60 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}}}}{2628 \left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}}-\frac {\left (\left (31130+6 i \sqrt {895302429}\right )^{\frac {4}{3}}+1986 \left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}+240 i \sqrt {895302429}+128560 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}+11574996\right ) c_{3} {\mathrm e}^{\frac {\left (\left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}+50 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}+3214\right ) t}{30 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}}}}{1314 \left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}} q \left (t \right ) = -\frac {5 \left (i \sqrt {3}\, \left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}-3214 i \sqrt {3}+\left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}+20 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}+3214\right ) c_{1} {\mathrm e}^{-\frac {\left (i \sqrt {3}\, \left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}-3214 i \sqrt {3}+\left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}-100 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}+3214\right ) t}{60 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}}}}{219 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}}+\frac {5 \left (i \sqrt {3}\, \left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}-3214 i \sqrt {3}-\left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}-20 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}-3214\right ) c_{2} {\mathrm e}^{\frac {\left (i \sqrt {3}\, \left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}-3214 i \sqrt {3}-\left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}+100 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}-3214\right ) t}{60 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}}}}{219 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}}+\frac {10 \left (\left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}-10 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}+3214\right ) c_{3} {\mathrm e}^{\frac {\left (\left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}+50 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}+3214\right ) t}{30 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}}}}{219 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}} r \left (t \right ) = c_{1} {\mathrm e}^{-\frac {\left (i \sqrt {3}\, \left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}-3214 i \sqrt {3}+\left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}-100 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}+3214\right ) t}{60 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}}}+c_{2} {\mathrm e}^{\frac {\left (i \sqrt {3}\, \left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}-3214 i \sqrt {3}-\left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}+100 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}-3214\right ) t}{60 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}}}+c_{3} {\mathrm e}^{\frac {\left (\left (31130+6 i \sqrt {895302429}\right )^{\frac {2}{3}}+50 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}+3214\right ) t}{30 \left (31130+6 i \sqrt {895302429}\right )^{\frac {1}{3}}}} \end{align*}
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 602
DSolve[{p'[t]==3*p[t]-2*q[t]-7*r[t],q'[t]==-2*p[t]+6*r[t],r'[t]==73/100*q[t]+2*r[t]},{p[t],q[t],r[t]},t,IncludeSingularSolutions -> True]
\begin{align*} p(t)\to -100 c_2 \text {RootSum}\left [\text {$\#$1}^3-500 \text {$\#$1}^2-23800 \text {$\#$1}+10920000\&,\frac {2 \text {$\#$1} e^{\frac {\text {$\#$1} t}{100}}+111 e^{\frac {\text {$\#$1} t}{100}}}{3 \text {$\#$1}^2-1000 \text {$\#$1}-23800}\&\right ]-100 c_3 \text {RootSum}\left [\text {$\#$1}^3-500 \text {$\#$1}^2-23800 \text {$\#$1}+10920000\&,\frac {7 \text {$\#$1} e^{\frac {\text {$\#$1} t}{100}}+1200 e^{\frac {\text {$\#$1} t}{100}}}{3 \text {$\#$1}^2-1000 \text {$\#$1}-23800}\&\right ]+c_1 \text {RootSum}\left [\text {$\#$1}^3-500 \text {$\#$1}^2-23800 \text {$\#$1}+10920000\&,\frac {\text {$\#$1}^2 e^{\frac {\text {$\#$1} t}{100}}-200 \text {$\#$1} e^{\frac {\text {$\#$1} t}{100}}-43800 e^{\frac {\text {$\#$1} t}{100}}}{3 \text {$\#$1}^2-1000 \text {$\#$1}-23800}\&\right ] q(t)\to -200 c_1 \text {RootSum}\left [\text {$\#$1}^3-500 \text {$\#$1}^2-23800 \text {$\#$1}+10920000\&,\frac {\text {$\#$1} e^{\frac {\text {$\#$1} t}{100}}-200 e^{\frac {\text {$\#$1} t}{100}}}{3 \text {$\#$1}^2-1000 \text {$\#$1}-23800}\&\right ]+200 c_3 \text {RootSum}\left [\text {$\#$1}^3-500 \text {$\#$1}^2-23800 \text {$\#$1}+10920000\&,\frac {3 \text {$\#$1} e^{\frac {\text {$\#$1} t}{100}}-200 e^{\frac {\text {$\#$1} t}{100}}}{3 \text {$\#$1}^2-1000 \text {$\#$1}-23800}\&\right ]+c_2 \text {RootSum}\left [\text {$\#$1}^3-500 \text {$\#$1}^2-23800 \text {$\#$1}+10920000\&,\frac {\text {$\#$1}^2 e^{\frac {\text {$\#$1} t}{100}}-500 \text {$\#$1} e^{\frac {\text {$\#$1} t}{100}}+60000 e^{\frac {\text {$\#$1} t}{100}}}{3 \text {$\#$1}^2-1000 \text {$\#$1}-23800}\&\right ] r(t)\to -14600 c_1 \text {RootSum}\left [\text {$\#$1}^3-500 \text {$\#$1}^2-23800 \text {$\#$1}+10920000\&,\frac {e^{\frac {\text {$\#$1} t}{100}}}{3 \text {$\#$1}^2-1000 \text {$\#$1}-23800}\&\right ]+73 c_2 \text {RootSum}\left [\text {$\#$1}^3-500 \text {$\#$1}^2-23800 \text {$\#$1}+10920000\&,\frac {\text {$\#$1} e^{\frac {\text {$\#$1} t}{100}}-300 e^{\frac {\text {$\#$1} t}{100}}}{3 \text {$\#$1}^2-1000 \text {$\#$1}-23800}\&\right ]+c_3 \text {RootSum}\left [\text {$\#$1}^3-500 \text {$\#$1}^2-23800 \text {$\#$1}+10920000\&,\frac {\text {$\#$1}^2 e^{\frac {\text {$\#$1} t}{100}}-300 \text {$\#$1} e^{\frac {\text {$\#$1} t}{100}}-40000 e^{\frac {\text {$\#$1} t}{100}}}{3 \text {$\#$1}^2-1000 \text {$\#$1}-23800}\&\right ] \end{align*}