Internal problem ID [6729]
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 }\left (t \right )&=-4 x \left (t \right )+2 y\\ y^{\prime }&=-\frac {5 x \left (t \right )}{2}+2 y \end {align*}
✓ Solution by Maple
Time used: 0.016 (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)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{-3 t} \\ y \left (t \right ) &= \frac {5 c_{1} {\mathrm e}^{t}}{2}+\frac {c_{2} {\mathrm e}^{-3 t}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 149
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}{28} e^{-\left (\left (1+\sqrt {14}\right ) t\right )} \left (c_1 \left (\left (14-3 \sqrt {14}\right ) e^{2 \sqrt {14} t}+14+3 \sqrt {14}\right )+2 \sqrt {14} c_2 \left (e^{2 \sqrt {14} t}-1\right )\right ) \\ y(t)\to \frac {1}{56} e^{-\left (\left (1+\sqrt {14}\right ) t\right )} \left (5 \sqrt {14} c_1 \left (e^{2 \sqrt {14} t}-1\right )+2 c_2 \left (\left (14+3 \sqrt {14}\right ) e^{2 \sqrt {14} t}+14-3 \sqrt {14}\right )\right ) \\ \end{align*}