Internal problem ID [356]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.6, Multiple Eigenvalue Solutions. Examples. Page 437
Problem number: Example 4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=x_{2} \left (t \right )+2 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-5 x_{1} \left (t \right )-3 x_{2} \left (t \right )-7 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=x_{1} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 75
dsolve([diff(x__1(t),t)=0*x__1(t)+1*x__2(t)+2*x__3(t),diff(x__2(t),t)=-5*x__1(t)-3*x__2(t)-7*x__3(t),diff(x__3(t),t)=1*x__1(t)+0*x__2(t)+0*x__3(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= -{\mathrm e}^{-t} \left (c_{3} t^{2}+c_{2} t -2 c_{3} t +c_{1} -c_{2} \right ) \\ x_{2} \left (t \right ) &= -{\mathrm e}^{-t} \left (c_{3} t^{2}+c_{2} t +4 c_{3} t +c_{1} +2 c_{2} -2 c_{3} \right ) \\ x_{3} \left (t \right ) &= {\mathrm e}^{-t} \left (c_{3} t^{2}+c_{2} t +c_{1} \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 134
DSolve[{x1'[t]==0*x1[t]+1*x2[t]+2*x3[t],x2'[t]==-5*x1[t]-3*x2[t]-7*x3[t],x3'[t]==1*x1[t]+0*x2[t]+0*x[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 (-2 t^2+2 t+2\right )-c_2 (t-2) t+c_3 (4-3 t) t\right ) \\ \text {x2}(t)\to \frac {1}{2} e^{-t} \left (-\left ((2 c_1+c_2+3 c_3) t^2\right )-2 (5 c_1+2 c_2+7 c_3) t+2 c_2\right ) \\ \text {x3}(t)\to \frac {1}{2} e^{-t} \left ((2 c_1+c_2+3 c_3) t^2+2 (c_1+c_3) t+2 c_3\right ) \\ \end{align*}