Internal problem ID [380]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.6, Multiple Eigenvalue Solutions. Page 451
Problem number: problem 23.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=39 x_{1} \relax (t )+8 x_{2} \relax (t )-16 x_{3} \relax (t )\\ x_{2}^{\prime }\relax (t )&=-36 x_{1} \relax (t )-5 x_{2} \relax (t )+16 x_{3} \relax (t )\\ x_{3}^{\prime }\relax (t )&=72 x_{1} \relax (t )+16 x_{2} \relax (t )-29 x_{3} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 67
dsolve([diff(x__1(t),t)=39*x__1(t)+8*x__2(t)-16*x__3(t),diff(x__2(t),t)=-36*x__1(t)-5*x__2(t)+16*x__3(t),diff(x__3(t),t)=72*x__1(t)+16*x__2(t)-29*x__3(t)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1} \relax (t ) = \frac {5 c_{2} {\mathrm e}^{3 t}}{9}+\frac {c_{3} {\mathrm e}^{-t}}{2}-\frac {2 c_{1} {\mathrm e}^{3 t}}{9} \] \[ x_{2} \relax (t ) = -\frac {c_{2} {\mathrm e}^{3 t}}{2}-\frac {c_{3} {\mathrm e}^{-t}}{2}+c_{1} {\mathrm e}^{3 t} \] \[ x_{3} \relax (t ) = c_{2} {\mathrm e}^{3 t}+c_{3} {\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 113
DSolve[{x1'[t]==39*x1[t]+8*x2[t]-16*x3[t],x2'[t]==-36*x1[t]-5*x2[t]+16*x3[t],x3'[t]==72*x1[t]+16*x2[t]-29*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{-t} \left (c_1 \left (10 e^{4 t}-9\right )+2 (c_2-2 c_3) \left (e^{4 t}-1\right )\right ) \\ \text {x2}(t)\to e^{-t} \left (-(9 c_1+c_2-4 c_3) e^{4 t}+9 c_1+2 c_2-4 c_3\right ) \\ \text {x3}(t)\to e^t (c_3 \cosh (2 t)+(36 c_1+8 c_2-15 c_3) \sinh (2 t)) \\ \end{align*}