Internal problem ID [6756]
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: 33.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=6 x \left (t \right )-y\\ y^{\prime }&=5 x \left (t \right )+2 y \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 47
dsolve([diff(x(t),t)=6*x(t)-y(t),diff(y(t),t)=5*x(t)+2*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{4 t} \left (c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right )\right ) \\ y \left (t \right ) &= {\mathrm e}^{4 t} \left (-c_{1} \cos \left (t \right )+c_{2} \sin \left (t \right )+2 c_{1} \sin \left (t \right )+2 c_{2} \cos \left (t \right )\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 55
DSolve[{x'[t]==6*x[t]-y[t],y'[t]==5*x[t]+2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{4 t} (c_1 (2 \sin (t)+\cos (t))-c_2 \sin (t)) \\ y(t)\to e^{4 t} (c_2 \cos (t)+(5 c_1-2 c_2) \sin (t)) \\ \end{align*}