Internal problem ID [322]
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 8.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )-5 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )-x_{2} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 50
dsolve([diff(x__1(t),t)=x__1(t)-5*x__2(t),diff(x__2(t),t)=x__1(t)-x__2(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= c_{1} \sin \left (2 t \right )+c_{2} \cos \left (2 t \right ) \\ x_{2} \left (t \right ) &= -\frac {2 c_{1} \cos \left (2 t \right )}{5}+\frac {2 c_{2} \sin \left (2 t \right )}{5}+\frac {c_{1} \sin \left (2 t \right )}{5}+\frac {c_{2} \cos \left (2 t \right )}{5} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 48
DSolve[{x1'[t]==x1[t]-5*x2[t],x2'[t]==x1[t]-x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to c_1 \cos (2 t)+(c_1-5 c_2) \sin (t) \cos (t) \\ \text {x2}(t)\to c_2 \cos (2 t)+(c_1-c_2) \sin (t) \cos (t) \\ \end{align*}