Internal problem ID [12829]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 3. Linear Systems. Review Exercises for chapter 3. page 376
Problem number: 19(i).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )+y\\ y^{\prime }&=-2 x \left (t \right )-y \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 38
dsolve([diff(x(t),t)=1*x(t)+1*y(t),diff(y(t),t)=-2*x(t)-y(t)],[x(t), y(t)], singsol=all)
\begin{align*} x \left (t \right ) = -\frac {\cos \left (t \right ) c_{1}}{2}+\frac {\sin \left (t \right ) c_{2}}{2}-\frac {\sin \left (t \right ) c_{1}}{2}-\frac {\cos \left (t \right ) c_{2}}{2} y \left (t \right ) = \sin \left (t \right ) c_{1} +\cos \left (t \right ) c_{2} \end{align*}
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 39
DSolve[{x'[t]==1*x[t]+1*y[t],y'[t]==-2*x[t]-y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 \cos (t)+(c_1+c_2) \sin (t) y(t)\to c_2 \cos (t)-(2 c_1+c_2) \sin (t) \end{align*}