Internal problem ID [367]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.6, Multiple Eigenvalue Solutions. Page 451
Problem number: problem 10.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=-13 x_{1}\relax (t )+40 x_{2}\relax (t )-48 x_{3}\relax (t )\\ x_{2}^{\prime }\relax (t )&=-8 x_{1}\relax (t )+23 x_{2}\relax (t )-24 x_{3}\relax (t )\\ x_{3}^{\prime }\relax (t )&=3 x_{3}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.021 (sec). Leaf size: 52
dsolve([diff(x__1(t),t)=-13*x__1(t)+40*x__2(t)-48*x__3(t),diff(x__2(t),t)=-8*x__1(t)+23*x__2(t)-24*x__3(t),diff(x__3(t),t)=0*x__1(t)+0*x__2(t)+3*x__3(t)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1}\relax (t ) = \frac {5 c_{1} {\mathrm e}^{3 t}}{2}+2 c_{2} {\mathrm e}^{7 t}-3 \,{\mathrm e}^{3 t} c_{3} \] \[ x_{2}\relax (t ) = c_{1} {\mathrm e}^{3 t}+c_{2} {\mathrm e}^{7 t} \] \[ x_{3}\relax (t ) = {\mathrm e}^{3 t} c_{3} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 94
DSolve[{x1'[t]==-13*x1[t]+40*x2[t]-48*x3[t],x2'[t]==-8*x1[t]+23*x2[t]-24*x3[t],x3'[t]==0*x1[t]+0*x2[t]+3*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{3 t} \left (c_1 \left (5-4 e^{4 t}\right )+2 (5 c_2-6 c_3) \left (e^{4 t}-1\right )\right ) \\ \text {x2}(t)\to (-2 c_1+5 c_2-6 c_3) e^{7 t}+2 (c_1-2 c_2+3 c_3) e^{3 t} \\ \text {x3}(t)\to c_3 e^{3 t} \\ \end{align*}