Internal problem ID [364]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.6, Multiple Eigenvalue Solutions. Page 451
Problem number: problem 7.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=2 x_{1}\relax (t )\\ x_{2}^{\prime }\relax (t )&=-7 x_{1}\relax (t )+9 x_{2}\relax (t )+7 x_{3}\relax (t )\\ x_{3}^{\prime }\relax (t )&=2 x_{3}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.018 (sec). Leaf size: 38
dsolve([diff(x__1(t),t)=2*x__1(t)+0*x__2(t)+0*x__3(t),diff(x__2(t),t)=-7*x__1(t)+9*x__2(t)+7*x__3(t),diff(x__3(t),t)=0*x__1(t)+0*x__2(t)+2*x__3(t)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1}\relax (t ) = {\mathrm e}^{2 t} \left (c_{1}+c_{3}\right ) \] \[ x_{2}\relax (t ) = c_{1} {\mathrm e}^{2 t}+c_{2} {\mathrm e}^{9 t} \] \[ x_{3}\relax (t ) = c_{3} {\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 55
DSolve[{x1'[t]==2*x1[t]+0*x2[t]+0*x3[t],x2'[t]==-7*x1[t]+9*x2[t]+7*x3[t],x3'[t]==0*x1[t]+0*x2[t]+2*x3[t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to c_1 e^{2 t} \\ \text {x2}(t)\to e^{2 t} \left ((-c_1+c_2+c_3) e^{7 t}+c_1-c_3\right ) \\ \text {x3}(t)\to c_3 e^{2 t} \\ \end{align*}