Internal problem ID [6008]
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 }\relax (t )&=x \relax (t )-8 y \relax (t )\\ y^{\prime }\relax (t )&=x \relax (t )-3 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.058 (sec). Leaf size: 58
dsolve([diff(x(t),t)=x(t)-8*y(t),diff(y(t),t)=x(t)-3*y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = 2 \,{\mathrm e}^{-t} \left (\cos \left (2 t \right ) c_{1}+\cos \left (2 t \right ) c_{2}+\sin \left (2 t \right ) c_{1}-\sin \left (2 t \right ) c_{2}\right ) \] \[ y \relax (t ) = {\mathrm e}^{-t} \left (\sin \left (2 t \right ) c_{1}+\cos \left (2 t \right ) c_{2}\right ) \]
✓ 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*}