Internal problem ID [6723]
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: 13.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-x \left (t \right )+\frac {y}{4}\\ y^{\prime }&=x \left (t \right )-y \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 36
dsolve([diff(x(t),t)=-x(t)+1/4*y(t),diff(y(t),t)=x(t)-y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{-\frac {t}{2}}+c_{2} {\mathrm e}^{-\frac {3 t}{2}} \\ y \left (t \right ) &= 2 c_{1} {\mathrm e}^{-\frac {t}{2}}-2 c_{2} {\mathrm e}^{-\frac {3 t}{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 66
DSolve[{x'[t]==-x[t]+1/4*y[t],y'[t]==x[t]-y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{4} e^{-3 t/2} \left (2 c_1 \left (e^t+1\right )+c_2 \left (e^t-1\right )\right ) \\ y(t)\to \frac {1}{2} e^{-3 t/2} \left (2 c_1 \left (e^t-1\right )+c_2 \left (e^t+1\right )\right ) \\ \end{align*}