Internal problem ID [6760]
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: 37.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=4 x \left (t \right )-5 y\\ y^{\prime }&=5 x \left (t \right )-4 y \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 50
dsolve([diff(x(t),t)=4*x(t)-5*y(t),diff(y(t),t)=5*x(t)-4*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} \sin \left (3 t \right )+c_{2} \cos \left (3 t \right ) \\ y \left (t \right ) &= -\frac {3 c_{1} \cos \left (3 t \right )}{5}+\frac {3 c_{2} \sin \left (3 t \right )}{5}+\frac {4 c_{1} \sin \left (3 t \right )}{5}+\frac {4 c_{2} \cos \left (3 t \right )}{5} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 58
DSolve[{x'[t]==4*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 c_1 \cos (3 t)+\frac {1}{3} (4 c_1-5 c_2) \sin (3 t) \\ y(t)\to c_2 \cos (3 t)+\frac {1}{3} (5 c_1-4 c_2) \sin (3 t) \\ \end{align*}