Internal problem ID [13080]
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: 5.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-\frac {x \left (t \right )}{2}\\ y^{\prime }&=x \left (t \right )-\frac {y}{2} \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 24
dsolve([diff(x(t),t)=-1/2*x(t),diff(y(t),t)=x(t)-1/2*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{-\frac {t}{2}} \\ y \left (t \right ) &= \left (c_{2} t +c_{1} \right ) {\mathrm e}^{-\frac {t}{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 33
DSolve[{x'[t]==-1/2*x[t],y'[t]==x[t]-1/2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^{-t/2} \\ y(t)\to e^{-t/2} (c_1 t+c_2) \\ \end{align*}