Internal problem ID [10546]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY.
2015.
Section: Chapter 4, Linear Systems. Exercises page 237
Problem number: 6.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )-2 y \left (t \right )\\ y^{\prime }\left (t \right )&=-2 x \left (t \right )+4 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (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: 0.003 (sec). Leaf size: 59
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_1-2 c_2) e^{5 t}+4 c_1+2 c_2\right ) \\ y(t)\to \frac {1}{5} \left (-2 (c_1-2 c_2) e^{5 t}+2 c_1+c_2\right ) \\ \end{align*}