Internal problem ID [6732]
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: 6.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-6 x \left (t \right )+2 y\\ y^{\prime }&=-3 x \left (t \right )+y \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve([diff(x(t),t)=-6*x(t)+2*y(t),diff(y(t),t)=-3*x(t)+y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} +c_{2} {\mathrm e}^{-5 t} \\ y \left (t \right ) &= \frac {c_{2} {\mathrm e}^{-5 t}}{2}+3 c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 73
DSolve[{x'[t]==-6*x[t]+2*y[t],y'[t]==-3*x[t]+y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{5} e^{-5 t} \left (2 c_2 \left (e^{5 t}-1\right )-c_1 \left (e^{5 t}-6\right )\right ) \\ y(t)\to \frac {1}{5} e^{-5 t} \left (c_2 \left (6 e^{5 t}-1\right )-3 c_1 \left (e^{5 t}-1\right )\right ) \\ \end{align*}