Internal problem ID [375]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.6, Multiple Eigenvalue Solutions. Page 451
Problem number: problem 18.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=x_{1}\relax (t )\\ x_{2}^{\prime }\relax (t )&=x_{1}\relax (t )+3 x_{2}\relax (t )+x_{3}\relax (t )\\ x_{3}^{\prime }\relax (t )&=-2 x_{1}\relax (t )-4 x_{2}\relax (t )-x_{3}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.023 (sec). Leaf size: 43
dsolve([diff(x__1(t),t)=1*x__1(t)+0*x__2(t)-0*x__3(t),diff(x__2(t),t)=1*x__1(t)+3*x__2(t)+1*x__3(t),diff(x__3(t),t)=-2*x__1(t)-4*x__2(t)-1*x__3(t)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1}\relax (t ) = -\frac {{\mathrm e}^{t} \left (4 c_{1}+c_{3}\right )}{2} \] \[ x_{2}\relax (t ) = \frac {{\mathrm e}^{t} \left (-c_{3} t +2 c_{1}-c_{2}\right )}{2} \] \[ x_{3}\relax (t ) = {\mathrm e}^{t} \left (c_{3} t +c_{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 54
DSolve[{x1'[t]==1*x1[t]+0*x2[t]-0*x3[t],x2'[t]==1*x1[t]+3*x2[t]+1*x3[t],x3'[t]==-2*x1[t]-4*x2[t]-1*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to c_1 e^t \\ \text {x2}(t)\to e^t ((c_1+2 c_2+c_3) t+c_2) \\ \text {x3}(t)\to e^t (c_3-2 (c_1+2 c_2+c_3) t) \\ \end{align*}