Internal problem ID [13155]
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: 19 (vii).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=y\\ y^{\prime }&=-4 x \left (t \right )-4 y \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
dsolve([diff(x(t),t)=0*x(t)+1*y(t),diff(y(t),t)=-4*x(t)-4*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= \left (c_{2} t +c_{1} \right ) {\mathrm e}^{-2 t} \\ y \left (t \right ) &= -{\mathrm e}^{-2 t} \left (2 c_{2} t +2 c_{1} -c_{2} \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 45
DSolve[{x'[t]==0*x[t]+1*y[t],y'[t]==-4*x[t]-4*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-2 t} (2 c_1 t+c_2 t+c_1) \\ y(t)\to e^{-2 t} (c_2-2 (2 c_1+c_2) t) \\ \end{align*}