Internal problem ID [6004]
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 }\relax (t )&=x \relax (t )+y \relax (t )\\ y^{\prime }\relax (t )&=-2 x \relax (t )-y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 38
dsolve([diff(x(t),t)=x(t)+y(t),diff(y(t),t)=-2*x(t)-y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = -\frac {\cos \relax (t ) c_{1}}{2}+\frac {c_{2} \sin \relax (t )}{2}-\frac {\sin \relax (t ) c_{1}}{2}-\frac {\cos \relax (t ) c_{2}}{2} \] \[ y \relax (t ) = \cos \relax (t ) c_{2}+\sin \relax (t ) c_{1} \]
✓ Solution by Mathematica
Time used: 0.007 (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*}