Internal problem ID [6006]
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: 36.
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 )&=-2 x \relax (t )+6 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 59
dsolve([diff(x(t),t)=4*x(t)+5*y(t),diff(y(t),t)=-2*x(t)+6*y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = \frac {{\mathrm e}^{5 t} \left (\sin \left (3 t \right ) c_{1}+3 \sin \left (3 t \right ) c_{2}-3 \cos \left (3 t \right ) c_{1}+\cos \left (3 t \right ) c_{2}\right )}{2} \] \[ y \relax (t ) = {\mathrm e}^{5 t} \left (\sin \left (3 t \right ) c_{1}+\cos \left (3 t \right ) c_{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 69
DSolve[{x'[t]==4*x[t]+5*y[t],y'[t]==-2*x[t]+6*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{3} e^{5 t} (3 c_1 \cos (3 t)-(c_1-5 c_2) \sin (3 t)) \\ y(t)\to \frac {1}{3} e^{5 t} (3 c_2 \cos (3 t)+(c_2-2 c_1) \sin (3 t)) \\ \end{align*}