Internal problem ID [12253]
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: 2.5.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=x-5 y \left (t \right )\\ y^{\prime }\left (t \right )&=x-y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 48
dsolve([diff(x(t),t)=x(t)-5*y(t),diff(y(t),t)=x(t)-y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = 2 c_{1} \cos \left (2 t \right )-2 c_{2} \sin \left (2 t \right )+c_{1} \sin \left (2 t \right )+c_{2} \cos \left (2 t \right ) \] \[ y \left (t \right ) = c_{1} \sin \left (2 t \right )+c_{2} \cos \left (2 t \right ) \]
✓ 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*}