Internal problem ID [12365]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A.
Dobrushkin. CRC Press 2015
Section: Chapter 6. Introduction to Systems of ODEs. Problems page 408
Problem number: Problem 3(d).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-5 x \left (t \right )+2 y\\ y^{\prime }&=-2 x \left (t \right )+y \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 83
dsolve([diff(x(t),t)+5*x(t)-2*y(t)=0,diff(y(t),t)+2*x(t)-y(t)=0],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{\left (-2+\sqrt {5}\right ) t}+c_{2} {\mathrm e}^{-\left (2+\sqrt {5}\right ) t} \\ y \left (t \right ) &= \frac {c_{1} {\mathrm e}^{\left (-2+\sqrt {5}\right ) t} \sqrt {5}}{2}-\frac {c_{2} {\mathrm e}^{-\left (2+\sqrt {5}\right ) t} \sqrt {5}}{2}+\frac {3 c_{1} {\mathrm e}^{\left (-2+\sqrt {5}\right ) t}}{2}+\frac {3 c_{2} {\mathrm e}^{-\left (2+\sqrt {5}\right ) t}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 148
DSolve[{x'[t]+5*x[t]-2*y[t]==0,y'[t]+2*x[t]-y[t]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{10} e^{-\left (\left (2+\sqrt {5}\right ) t\right )} \left (c_1 \left (\left (5-3 \sqrt {5}\right ) e^{2 \sqrt {5} t}+5+3 \sqrt {5}\right )+2 \sqrt {5} c_2 \left (e^{2 \sqrt {5} t}-1\right )\right ) \\ y(t)\to \frac {1}{10} e^{-\left (\left (2+\sqrt {5}\right ) t\right )} \left (c_2 \left (\left (5+3 \sqrt {5}\right ) e^{2 \sqrt {5} t}+5-3 \sqrt {5}\right )-2 \sqrt {5} c_1 \left (e^{2 \sqrt {5} t}-1\right )\right ) \\ \end{align*}