Internal problem ID [5991]
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: 20.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-6 x \left (t \right )+5 y \left (t \right )\\ y^{\prime }\left (t \right )&=-5 x \left (t \right )+4 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 35
dsolve([diff(x(t),t)=-6*x(t)+5*y(t),diff(y(t),t)=-5*x(t)+4*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = \frac {{\mathrm e}^{-t} \left (5 c_{2} t +5 c_{1} -c_{2} \right )}{5} \] \[ y \left (t \right ) = {\mathrm e}^{-t} \left (c_{2} t +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 46
DSolve[{x'[t]==-6*x[t]+5*y[t],y'[t]==-5*x[t]+4*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-t} (-5 c_1 t+5 c_2 t+c_1) \\ y(t)\to e^{-t} (5 (c_2-c_1) t+c_2) \\ \end{align*}