Internal problem ID [11017]
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 \left (t \right )\\ y^{\prime }\left (t \right )&=-2 x \left (t \right )+y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (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],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -\frac {c_{1} {\mathrm e}^{\left (-2+\sqrt {5}\right ) t} \sqrt {5}}{2}+\frac {c_{2} {\mathrm e}^{-\left (2+\sqrt {5}\right ) t} \sqrt {5}}{2}+\frac {3 c_{1} {\mathrm e}^{\left (-2+\sqrt {5}\right ) t}}{2}+\frac {3 c_{2} {\mathrm e}^{-\left (2+\sqrt {5}\right ) t}}{2} \] \[ y \left (t \right ) = c_{1} {\mathrm e}^{\left (-2+\sqrt {5}\right ) t}+c_{2} {\mathrm e}^{-\left (2+\sqrt {5}\right ) t} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 98
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}{5} e^{-2 t} \left (5 c_1 \cosh \left (\sqrt {5} t\right )+\sqrt {5} (2 c_2-3 c_1) \sinh \left (\sqrt {5} t\right )\right ) \\ y(t)\to \frac {1}{5} e^{-2 t} \left (5 c_2 \cosh \left (\sqrt {5} t\right )+\sqrt {5} (3 c_2-2 c_1) \sinh \left (\sqrt {5} t\right )\right ) \\ \end{align*}