72.15.10 problem 19 (vii)

Internal problem ID [14891]
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)
Date solved : Tuesday, January 28, 2025 at 07:18:12 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=y\\ y^{\prime }&=-4 x \left (t \right )-4 y \end{align*}

✓ Solution by Maple

Time used: 0.042 (sec). Leaf size: 34

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 &= -{\mathrm e}^{-2 t} \left (2 c_{2} t +2 c_{1} -c_{2} \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 45

DSolve[{D[x[t],t]==0*x[t]+1*y[t],D[y[t],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*}