Internal problem ID [11543]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 4, Linear Systems. Exercises page 190
Problem number: 2(c).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=-3 x\\ y^{\prime }\left (t \right )&=2 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 20
dsolve([diff(x(t),t)=-3*x(t),diff(y(t),t)=2*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = {\mathrm e}^{-3 t} c_{1} \] \[ y \left (t \right ) = c_{2} {\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.067 (sec). Leaf size: 65
DSolve[{x'[t]==-3*x[t],y'[t]==3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^{-3 t} y(t)\to c_2 e^{3 t} x(t)\to c_1 e^{-3 t} y(t)\to 0 x(t)\to 0 y(t)\to c_2 e^{3 t} x(t)\to 0 y(t)\to 0 \end{align*}