Internal problem ID [383]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.6, Multiple Eigenvalue Solutions. Page 451
Problem number: problem 26.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=5 x_{1}\relax (t )-x_{2}\relax (t )+x_{3}\relax (t )\\ x_{2}^{\prime }\relax (t )&=x_{1}\relax (t )+3 x_{2}\relax (t )\\ x_{3}^{\prime }\relax (t )&=-3 x_{1}\relax (t )+2 x_{2}\relax (t )+x_{3}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.018 (sec). Leaf size: 65
dsolve([diff(x__1(t),t)=5*x__1(t)-1*x__2(t)+1*x__3(t),diff(x__2(t),t)=1*x__1(t)+3*x__2(t)+0*x__3(t),diff(x__3(t),t)=-3*x__1(t)+2*x__2(t)+1*x__3(t)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1}\relax (t ) = {\mathrm e}^{3 t} \left (2 c_{3} t +c_{2}+4 c_{3}\right ) \] \[ x_{2}\relax (t ) = {\mathrm e}^{3 t} \left (c_{3} t^{2}+c_{2} t +4 c_{3} t +c_{1}+2 c_{2}+6 c_{3}\right ) \] \[ x_{3}\relax (t ) = {\mathrm e}^{3 t} \left (c_{3} t^{2}+c_{2} t +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 102
DSolve[{x1'[t]==5*x1[t]-1*x2[t]+1*x3[t],x2'[t]==1*x1[t]+3*x2[t]+0*x3[t],x3'[t]==-3*x1[t]+2*x2[t]+1*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{3 t} (2 c_1 t-c_2 t+c_3 t+c_1) \\ \text {x2}(t)\to \frac {1}{2} e^{3 t} (t (2 c_1 (t+1)+(c_3-c_2) t)+2 c_2) \\ \text {x3}(t)\to \frac {1}{2} e^{3 t} (2 c_1 (t-3) t-(c_2-c_3) (t-4) t+2 c_3) \\ \end{align*}