Internal problem ID [371]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.6, Multiple Eigenvalue Solutions. Page 451
Problem number: problem 14.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-5 x_{1} \left (t \right )-x_{2} \left (t \right )-5 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 72
dsolve([diff(x__1(t),t)=0*x__1(t)+0*x__2(t)+1*x__3(t),diff(x__2(t),t)=-5*x__1(t)-1*x__2(t)-5*x__3(t),diff(x__3(t),t)=4*x__1(t)+1*x__2(t)-2*x__3(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{-t} \left (c_{3} t^{2}+c_{2} t +c_{1} \right ) \\ x_{2} \left (t \right ) &= -{\mathrm e}^{-t} \left (5 c_{3} t^{2}+5 c_{2} t +5 c_{1} -2 c_{3} \right ) \\ x_{3} \left (t \right ) &= -{\mathrm e}^{-t} \left (c_{3} t^{2}+c_{2} t -2 c_{3} t +c_{1} -c_{2} \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 119
DSolve[{x1'[t]==0*x1[t]+0*x2[t]+1*x3[t],x2'[t]==-5*x1[t]-1*x2[t]-5*x3[t],x3'[t]==4*x1[t]+1*x2[t]-2*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{2} e^{-t} \left (c_1 \left (5 t^2+2 t+2\right )+t (c_2 t+2 c_3)\right ) \\ \text {x2}(t)\to \frac {1}{2} e^{-t} \left (-5 (5 c_1+c_2) t^2-10 (c_1+c_3) t+2 c_2\right ) \\ \text {x3}(t)\to \frac {1}{2} e^{-t} \left (-\left ((5 c_1+c_2) t^2\right )+2 (4 c_1+c_2-c_3) t+2 c_3\right ) \\ \end{align*}