Internal problem ID [5976]
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: 3.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=-4 x \relax (t )+2 y \relax (t )\\ y^{\prime }\relax (t )&=-\frac {5 x \relax (t )}{2}+2 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.053 (sec). Leaf size: 32
dsolve([diff(x(t),t)=-4*x(t)+2*y(t),diff(y(t),t)=-5/2*x(t)+2*y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = 2 c_{1} {\mathrm e}^{-3 t}+\frac {2 c_{2} {\mathrm e}^{t}}{5} \] \[ y \relax (t ) = c_{1} {\mathrm e}^{-3 t}+c_{2} {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 98
DSolve[{x'[t]==-4*x[t]+2*y[t],y'[t]==5/2*x[t]+2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{14} e^{-t} \left (14 c_1 \cosh \left (\sqrt {14} t\right )+\sqrt {14} (2 c_2-3 c_1) \sinh \left (\sqrt {14} t\right )\right ) \\ y(t)\to \frac {1}{28} e^{-t} \left (28 c_2 \cosh \left (\sqrt {14} t\right )+\sqrt {14} (5 c_1+6 c_2) \sinh \left (\sqrt {14} t\right )\right ) \\ \end{align*}