Internal problem ID [6007]
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 }\relax (t )&=4 x \relax (t )-5 y \relax (t )\\ y^{\prime }\relax (t )&=5 x \relax (t )-4 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.094 (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)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = \frac {3 \cos \left (3 t \right ) c_{1}}{5}-\frac {3 \sin \left (3 t \right ) c_{2}}{5}+\frac {4 \sin \left (3 t \right ) c_{1}}{5}+\frac {4 \cos \left (3 t \right ) c_{2}}{5} \] \[ y \relax (t ) = \sin \left (3 t \right ) c_{1}+\cos \left (3 t \right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.008 (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*}