Internal problem ID [368]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.6, Multiple Eigenvalue Solutions. Page 451
Problem number: problem 11.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=-3 x_{1} \relax (t )-4 x_{3} \relax (t )\\ x_{2}^{\prime }\relax (t )&=-x_{1} \relax (t )-x_{2} \relax (t )-x_{3} \relax (t )\\ x_{3}^{\prime }\relax (t )&=x_{1} \relax (t )+x_{3} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 61
dsolve([diff(x__1(t),t)=-3*x__1(t)+0*x__2(t)-4*x__3(t),diff(x__2(t),t)=-1*x__1(t)-1*x__2(t)-1*x__3(t),diff(x__3(t),t)=1*x__1(t)+0*x__2(t)+1*x__3(t)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1} \relax (t ) = -{\mathrm e}^{-t} \left (2 t c_{3}+2 c_{2}-c_{3}\right ) \] \[ x_{2} \relax (t ) = \frac {\left (t^{2} c_{3}+2 t c_{2}-2 t c_{3}+2 c_{1}\right ) {\mathrm e}^{-t}}{2} \] \[ x_{3} \relax (t ) = {\mathrm e}^{-t} \left (t c_{3}+c_{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 77
DSolve[{x1'[t]==-3*x1[t]+0*x2[t]-4*x3[t],x2'[t]==-1*x1[t]-1*x2[t]-1*x3[t],x3'[t]==1*x1[t]+0*x2[t]+1*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{-t} (-2 c_1 t-4 c_3 t+c_1) \\ \text {x2}(t)\to \frac {1}{2} e^{-t} (c_1 (t-2) t+2 c_3 (t-1) t+2 c_2) \\ \text {x3}(t)\to e^{-t} ((c_1+2 c_3) t+c_3) \\ \end{align*}