Internal problem ID [374]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.6, Multiple Eigenvalue Solutions. Page 451
Problem number: problem 17.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=x_{1}\relax (t )\\ x_{2}^{\prime }\relax (t )&=18 x_{1}\relax (t )+7 x_{2}\relax (t )+4 x_{3}\relax (t )\\ x_{3}^{\prime }\relax (t )&=-27 x_{1}\relax (t )-9 x_{2}\relax (t )-5 x_{3}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.021 (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)=18*x__1(t)+7*x__2(t)+4*x__3(t),diff(x__3(t),t)=-27*x__1(t)-9*x__2(t)-5*x__3(t)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1}\relax (t ) = -\frac {{\mathrm e}^{t} \left (9 c_{1}+c_{3}\right )}{27} \] \[ x_{2}\relax (t ) = \frac {{\mathrm e}^{t} \left (-2 c_{3} t +3 c_{1}-2 c_{2}\right )}{3} \] \[ x_{3}\relax (t ) = {\mathrm e}^{t} \left (c_{3} t +c_{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 63
DSolve[{x1'[t]==1*x1[t]+0*x2[t]-0*x3[t],x2'[t]==18*x1[t]+7*x2[t]+4*x3[t],x3'[t]==-27*x1[t]-9*x2[t]-5*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 (2 (9 c_1+3 c_2+2 c_3) t+c_2) \\ \text {x3}(t)\to e^t (c_3-3 (9 c_1+3 c_2+2 c_3) t) \\ \end{align*}