Internal problem ID [382]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.6, Multiple Eigenvalue Solutions. Page 451
Problem number: problem 25.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=-2 x_{1} \relax (t )+17 x_{2} \relax (t )+4 x_{3} \relax (t )\\ x_{2}^{\prime }\relax (t )&=-x_{1} \relax (t )+6 x_{2} \relax (t )+x_{3} \relax (t )\\ x_{3}^{\prime }\relax (t )&=x_{2} \relax (t )+2 x_{3} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 62
dsolve([diff(x__1(t),t)=-2*x__1(t)+17*x__2(t)+4*x__3(t),diff(x__2(t),t)=-1*x__1(t)+6*x__2(t)+1*x__3(t),diff(x__3(t),t)=0*x__1(t)+1*x__2(t)+2*x__3(t)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1} \relax (t ) = {\mathrm e}^{2 t} \left (t^{2} c_{3}+t c_{2}+8 t c_{3}+c_{1}+4 c_{2}-2 c_{3}\right ) \] \[ x_{2} \relax (t ) = {\mathrm e}^{2 t} \left (2 t c_{3}+c_{2}\right ) \] \[ x_{3} \relax (t ) = {\mathrm e}^{2 t} \left (t^{2} c_{3}+t c_{2}+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 104
DSolve[{x1'[t]==-2*x1[t]+17*x2[t]+4*x3[t],x2'[t]==-1*x1[t]+6*x2[t]+1*x3[t],x3'[t]==0*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^{2 t} (-(c_1 (t (t+8)-2))+c_2 t (4 t+34)+c_3 t (t+8)) \\ \text {x2}(t)\to e^{2 t} ((-c_1+4 c_2+c_3) t+c_2) \\ \text {x3}(t)\to \frac {1}{2} e^{2 t} \left ((-c_1+4 c_2+c_3) t^2+2 c_2 t+2 c_3\right ) \\ \end{align*}