Internal problem ID [5971]
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 8.1. Page 332
Problem number: 14.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=2 x \relax (t )+y \relax (t )\\ y^{\prime }\relax (t )&=-x \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.049 (sec). Leaf size: 26
dsolve([diff(x(t),t)=2*x(t)+y(t),diff(y(t),t)=-x(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = -{\mathrm e}^{t} \left (c_{2} t +c_{1}+c_{2}\right ) \] \[ y \relax (t ) = {\mathrm e}^{t} \left (c_{2} t +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 38
DSolve[{x'[t]==2*x[t]+y[t],y'[t]==-x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^t (c_1 (t+1)+c_2 t) \\ y(t)\to e^t (c_2-(c_1+c_2) t) \\ \end{align*}