Internal problem ID [12555]
Book: Nonlinear Ordinary Differential Equations by D.W.Jordna and P.Smith. 4th edition 1999.
Oxford Univ. Press. NY
Section: Chapter 2. Plane autonomous systems and linearization. Problems page 79
Problem number: 2.1 (i).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )-5 y \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right )-y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 50
dsolve([diff(x(t),t)=x(t)-5*y(t),diff(y(t),t)=x(t)-y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} \sin \left (2 t \right )+c_{2} \cos \left (2 t \right ) \\ y \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: 0.009 (sec). Leaf size: 48
DSolve[{x'[t]==x[t]-5*y[t],y'[t]==x[t]-y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 \cos (2 t)+(c_1-5 c_2) \sin (t) \cos (t) \\ y(t)\to c_2 \cos (2 t)+(c_1-c_2) \sin (t) \cos (t) \\ \end{align*}