Internal problem ID [14926]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 6. Systems of Differential Equations. Exercises 6.1, page 282
Problem number: 9.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=-x-2 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: 38
dsolve([diff(x(t),t)=-x(t)-2*y(t),diff(y(t),t)=x(t)+y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right ) \\ y \left (t \right ) &= -\frac {c_{1} \cos \left (t \right )}{2}+\frac {c_{2} \sin \left (t \right )}{2}-\frac {c_{1} \sin \left (t \right )}{2}-\frac {c_{2} \cos \left (t \right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 39
DSolve[{x'[t]==-x[t]-2*y[t],y'[t]==x[t]+y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 \cos (t)-(c_1+2 c_2) \sin (t) \\ y(t)\to c_2 \cos (t)+(c_1+c_2) \sin (t) \\ \end{align*}