Internal problem ID [327]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.3, The eigenvalue method for linear systems. Page 395
Problem number: problem 13.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=5 x_{1} \left (t \right )-9 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 58
dsolve([diff(x__1(t),t)=5*x__1(t)-9*x__2(t),diff(x__2(t),t)=2*x__1(t)-x__2(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{2 t} \left (c_{1} \sin \left (3 t \right )+c_{2} \cos \left (3 t \right )\right ) \\ x_{2} \left (t \right ) &= \frac {{\mathrm e}^{2 t} \left (c_{1} \sin \left (3 t \right )+c_{2} \sin \left (3 t \right )-c_{1} \cos \left (3 t \right )+c_{2} \cos \left (3 t \right )\right )}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 66
DSolve[{x1'[t]==5*x1[t]-9*x2[t],x2'[t]==2*x1[t]-x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{2 t} (c_1 \cos (3 t)+(c_1-3 c_2) \sin (3 t)) \\ \text {x2}(t)\to \frac {1}{3} e^{2 t} (3 c_2 \cos (3 t)+(2 c_1-3 c_2) \sin (3 t)) \\ \end{align*}