Internal problem ID [6005]
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 }\left (t \right )&=4 x \left (t \right )+5 y \left (t \right )\\ y^{\prime }\left (t \right )&=-2 x \left (t \right )+6 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (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)
\[ x \left (t \right ) = \frac {{\mathrm e}^{5 t} \left (\sin \left (3 t \right ) c_{1} +3 \sin \left (3 t \right ) c_{2} -3 \cos \left (3 t \right ) c_{1} +\cos \left (3 t \right ) c_{2} \right )}{2} \] \[ y \left (t \right ) = {\mathrm e}^{5 t} \left (\sin \left (3 t \right ) c_{1} +\cos \left (3 t \right ) c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.006 (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*}