Internal problem ID [12825]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 3. Linear Systems. Review Exercises for chapter 3. page 376
Problem number: 3.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=3 x \left (t \right )\\ y^{\prime }&=-2 y \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve([diff(x(t),t)=3*x(t)+0*y(t),diff(y(t),t)=0*x(t)-2*y(t)],[x(t), y(t)], singsol=all)
\begin{align*} x \left (t \right ) = c_{1} {\mathrm e}^{3 t} y \left (t \right ) = c_{2} {\mathrm e}^{-2 t} \end{align*}
✓ Solution by Mathematica
Time used: 0.064 (sec). Leaf size: 65
DSolve[{x'[t]==3*x[t]+0*y[t],y'[t]==0*x[t]-2*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^{-2 t} x(t)\to c_1 e^{3 t} y(t)\to 0 x(t)\to 0 y(t)\to c_2 e^{-2 t} x(t)\to 0 y(t)\to 0 \end{align*}