Internal problem ID [6761]
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: 38.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )-8 y\\ y^{\prime }&=x \left (t \right )-3 y \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 58
dsolve([diff(x(t),t)=x(t)-8*y(t),diff(y(t),t)=x(t)-3*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{-t} \left (c_{1} \sin \left (2 t \right )+c_{2} \cos \left (2 t \right )\right ) \\ y \left (t \right ) &= \frac {{\mathrm e}^{-t} \left (c_{1} \sin \left (2 t \right )+c_{2} \sin \left (2 t \right )-c_{1} \cos \left (2 t \right )+c_{2} \cos \left (2 t \right )\right )}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 64
DSolve[{x'[t]==x[t]-8*y[t],y'[t]==x[t]-3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-t} (c_1 \cos (2 t)+(c_1-4 c_2) \sin (2 t)) \\ y(t)\to \frac {1}{2} e^{-t} (2 c_2 \cos (2 t)+(c_1-2 c_2) \sin (2 t)) \\ \end{align*}