Internal problem ID [6757]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 8 SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS.
EXERCISES 8.2. Page 346
Problem number: 34.
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: 37
dsolve([diff(x(t),t)=x(t)+y(t),diff(y(t),t)=-2*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 ) &= c_{1} \cos \left (t \right )-c_{2} \sin \left (t \right )-c_{1} \sin \left (t \right )-c_{2} \cos \left (t \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 39
DSolve[{x'[t]==x[t]+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*}