Internal problem ID [10522]
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(b).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-3 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: 0.063 (sec). Leaf size: 36
dsolve([diff(x(t),t)=-3*y(t),diff(y(t),t)=-2*x(t)+y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -c_{1} {\mathrm e}^{3 t}+\frac {3 c_{2} {\mathrm e}^{-2 t}}{2} \] \[ y \left (t \right ) = c_{1} {\mathrm e}^{3 t}+c_{2} {\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 72
DSolve[{x'[t]==-3*y[t],y'[t]==-2*x[t]+y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{5} e^{-2 t} \left ((2 c_1-3 c_2) e^{5 t}+3 (c_1+c_2)\right ) \\ y(t)\to \frac {1}{5} e^{-2 t} \left ((3 c_2-2 c_1) e^{5 t}+2 (c_1+c_2)\right ) \\ \end{align*}