Internal problem ID [11016]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 6. Introduction to Systems of ODEs. Problems page 408
Problem number: Problem 3(c).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )-2 y \left (t \right )\\ y^{\prime }\left (t \right )&=-y \left (t \right )+x \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
dsolve([diff(x(t),t)-x(t)+2*y(t)=0,diff(y(t),t)+y(t)-x(t)=0],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = c_{1} \cos \left (t \right )-c_{2} \sin \left (t \right )+c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right ) \] \[ y \left (t \right ) = c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 39
DSolve[{x'[t]-x[t]+2*y[t]==0,y'[t]+y[t]-x[t]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 (\sin (t)+\cos (t))-2 c_2 \sin (t) \\ y(t)\to c_2 \cos (t)+(c_1-c_2) \sin (t) \\ \end{align*}