Internal problem ID [385]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.6, Multiple Eigenvalue Solutions. Page 451
Problem number: problem 28.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=-15 x_{1} \relax (t )-7 x_{2} \relax (t )+4 x_{3} \relax (t )\\ x_{2}^{\prime }\relax (t )&=34 x_{1} \relax (t )+16 x_{2} \relax (t )-11 x_{3} \relax (t )\\ x_{3}^{\prime }\relax (t )&=17 x_{1} \relax (t )+7 x_{2} \relax (t )+5 x_{3} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 75
dsolve([diff(x__1(t),t)=-15*x__1(t)-7*x__2(t)+4*x__3(t),diff(x__2(t),t)=34*x__1(t)+16*x__2(t)-11*x__3(t),diff(x__3(t),t)=17*x__1(t)+7*x__2(t)+5*x__3(t)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1} \relax (t ) = -\frac {{\mathrm e}^{2 t} \left (-119 t^{2} c_{3}-238 t c_{2}+34 t c_{3}+14 c_{1}+6 c_{2}-2 c_{3}\right )}{34} \] \[ x_{2} \relax (t ) = \frac {\left (-17 t^{2} c_{3}-34 t c_{2}+4 t c_{3}+2 c_{1}\right ) {\mathrm e}^{2 t}}{2} \] \[ x_{3} \relax (t ) = {\mathrm e}^{2 t} \left (t c_{3}+c_{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 118
DSolve[{x1'[t]==-15*x1[t]-7*x2[t]+4*x3[t],x2'[t]==34*x1[t]+16*x2[t]-11*x3[t],x3'[t]==17*x1[t]+7*x2[t]+5*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 (17 t (7 t-2)+2)+7 c_2 t (7 t-2)+c_3 t (21 t+8)) \\ \text {x2}(t)\to \frac {1}{2} e^{2 t} (-(17 c_1+7 c_2) t (17 t-4)-c_3 t (51 t+22)+2 c_2) \\ \text {x3}(t)\to e^{2 t} ((17 c_1+7 c_2+3 c_3) t+c_3) \\ \end{align*}