Internal problem ID [11553]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 4, Linear Systems. Exercises page 202
Problem number: 1(e).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=x-2 y \left (t \right )\\ y^{\prime }\left (t \right )&=-2 x+4 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 27
dsolve([diff(x(t),t)=x(t)-2*y(t),diff(y(t),t)=-2*x(t)+4*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -\frac {c_{2} {\mathrm e}^{5 t}}{2}+2 c_{1} \] \[ y \left (t \right ) = c_{1} +c_{2} {\mathrm e}^{5 t} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 62
DSolve[{x'[t]==x[t]-2*y[t],y'[t]==-2*x[t]+4*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{5} \left (c_1 \left (e^{5 t}+4\right )-2 c_2 \left (e^{5 t}-1\right )\right ) y(t)\to \frac {1}{5} \left (c_2 \left (4 e^{5 t}+1\right )-2 c_1 \left (e^{5 t}-1\right )\right ) \end{align*}