Internal problem ID [13076]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 3. Linear Systems. Exercises section 3.2. page 277
Problem number: 1.
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: 0.015 (sec). Leaf size: 20
dsolve([diff(x(t),t)=3*x(t),diff(y(t),t)=-2*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{3 t} \\ y \left (t \right ) &= c_{1} {\mathrm e}^{-2 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 32
DSolve[{x'[t]==3*x[t],y'[t]==-2*x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^{3 t} \\ y(t)\to c_2-\frac {2}{3} c_1 \left (e^{3 t}-1\right ) \\ \end{align*}