Internal problem ID [6003]
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 }\relax (t )&=6 x \relax (t )-y \relax (t )\\ y^{\prime }\relax (t )&=5 x \relax (t )+2 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 48
dsolve([diff(x(t),t)=6*x(t)-y(t),diff(y(t),t)=5*x(t)+2*y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = \frac {{\mathrm e}^{4 t} \left (2 \sin \relax (t ) c_{1}-c_{2} \sin \relax (t )+\cos \relax (t ) c_{1}+2 \cos \relax (t ) c_{2}\right )}{5} \] \[ y \relax (t ) = {\mathrm e}^{4 t} \left (\cos \relax (t ) c_{2}+\sin \relax (t ) c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 54
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} (5 c_1 \sin (t)+c_2 (\cos (t)-2 \sin (t))) \\ \end{align*}