Internal problem ID [13156]
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 (viii).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-3 x \left (t \right )-3 y\\ y^{\prime }&=2 x \left (t \right )+y \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 78
dsolve([diff(x(t),t)=-3*x(t)-3*y(t),diff(y(t),t)=2*x(t)+1*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{-t} \left (c_{1} \sin \left (\sqrt {2}\, t \right )+c_{2} \cos \left (\sqrt {2}\, t \right )\right ) \\ y \left (t \right ) &= \frac {{\mathrm e}^{-t} \left (\sin \left (\sqrt {2}\, t \right ) \sqrt {2}\, c_{2} -\cos \left (\sqrt {2}\, t \right ) \sqrt {2}\, c_{1} -2 c_{1} \sin \left (\sqrt {2}\, t \right )-2 c_{2} \cos \left (\sqrt {2}\, t \right )\right )}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 91
DSolve[{x'[t]==-3*x[t]-3*y[t],y'[t]==2*x[t]+1*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} e^{-t} \left (2 c_1 \cos \left (\sqrt {2} t\right )-\sqrt {2} (2 c_1+3 c_2) \sin \left (\sqrt {2} t\right )\right ) \\ y(t)\to e^{-t} \left (c_2 \cos \left (\sqrt {2} t\right )+\sqrt {2} (c_1+c_2) \sin \left (\sqrt {2} t\right )\right ) \\ \end{align*}