Internal problem ID [5979]
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: 6.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=-6 x \relax (t )+2 y \relax (t )\\ y^{\prime }\relax (t )&=-3 x \relax (t )+y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.052 (sec). Leaf size: 27
dsolve([diff(x(t),t)=-6*x(t)+2*y(t),diff(y(t),t)=-3*x(t)+y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = 2 c_{2} {\mathrm e}^{-5 t}+\frac {c_{1}}{3} \] \[ y \relax (t ) = c_{1}+c_{2} {\mathrm e}^{-5 t} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 64
DSolve[{x'[t]==-6*x[t]+2*y[t],y'[t]==-3*x[t]+y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{5} \left ((6 c_1-2 c_2) e^{-5 t}-c_1+2 c_2\right ) \\ y(t)\to \frac {1}{5} \left ((3 c_1-c_2) e^{-5 t}-3 c_1+6 c_2\right ) \\ \end{align*}