Internal problem ID [13087]
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: 11 (b).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-2 x \left (t \right )-2 y\\ y^{\prime }&=-2 x \left (t \right )+y \end {align*}
With initial conditions \[ [x \left (0\right ) = 0, y \left (0\right ) = 1] \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve([diff(x(t),t) = -2*x(t)-2*y(t), diff(y(t),t) = -2*x(t)+y(t), x(0) = 0, y(0) = 1], singsol=all)
\begin{align*} x \left (t \right ) &= -\frac {2 \,{\mathrm e}^{2 t}}{5}+\frac {2 \,{\mathrm e}^{-3 t}}{5} \\ y \left (t \right ) &= \frac {4 \,{\mathrm e}^{2 t}}{5}+\frac {{\mathrm e}^{-3 t}}{5} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 42
DSolve[{x'[t]==-2*x[t]-2*y[t],y'[t]==-2*x[t]+y[t]},{x[0]==0,y[0]==1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\frac {2}{5} e^{-3 t} \left (e^{5 t}-1\right ) \\ y(t)\to \frac {1}{5} e^{-3 t} \left (4 e^{5 t}+1\right ) \\ \end{align*}