Internal problem ID [366]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.6, Multiple Eigenvalue Solutions. Page 451
Problem number: problem 9.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=-19 x_{1} \relax (t )+12 x_{2} \relax (t )+84 x_{3} \relax (t )\\ x_{2}^{\prime }\relax (t )&=5 x_{2} \relax (t )\\ x_{3}^{\prime }\relax (t )&=-8 x_{1} \relax (t )+4 x_{2} \relax (t )+33 x_{3} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 52
dsolve([diff(x__1(t),t)=-19*x__1(t)+12*x__2(t)+84*x__3(t),diff(x__2(t),t)=0*x__1(t)+5*x__2(t)+0*x__3(t),diff(x__3(t),t)=-8*x__1(t)+4*x__2(t)+33*x__3(t)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1} \relax (t ) = \frac {7 c_{2} {\mathrm e}^{5 t}}{2}+3 c_{3} {\mathrm e}^{9 t}+\frac {{\mathrm e}^{5 t} c_{1}}{2} \] \[ x_{2} \relax (t ) = {\mathrm e}^{5 t} c_{1} \] \[ x_{3} \relax (t ) = c_{2} {\mathrm e}^{5 t}+c_{3} {\mathrm e}^{9 t} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 90
DSolve[{x1'[t]==-19*x1[t]+12*x2[t]+84*x3[t],x2'[t]==0*x1[t]+5*x2[t]+0*x3[t],x3'[t]==-8*x1[t]+4*x2[t]+33*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{5 t} \left (c_1 \left (7-6 e^{4 t}\right )+3 (c_2+7 c_3) \left (e^{4 t}-1\right )\right ) \\ \text {x2}(t)\to c_2 e^{5 t} \\ \text {x3}(t)\to e^{5 t} \left ((-2 c_1+c_2+7 c_3) e^{4 t}+2 c_1-c_2-6 c_3\right ) \\ \end{align*}