Internal problem ID [12859]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 10. Applications of Systems of Equations. Exercises 10.2 page 432
Problem number: 3.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-x \left (t \right )-2 y \left (t \right )\\ y^{\prime }\left (t \right )&=2 x \left (t \right )-3 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 76
dsolve([diff(x(t),t)=-x(t)-2*y(t),diff(y(t),t)=2*x(t)-3*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{-2 t} \left (\sin \left (\sqrt {3}\, t \right ) c_{1} +\cos \left (\sqrt {3}\, t \right ) c_{2} \right ) \\ y \left (t \right ) &= \frac {{\mathrm e}^{-2 t} \left (\sqrt {3}\, \sin \left (\sqrt {3}\, t \right ) c_{2} -\sqrt {3}\, \cos \left (\sqrt {3}\, t \right ) c_{1} +\sin \left (\sqrt {3}\, t \right ) c_{1} +\cos \left (\sqrt {3}\, t \right ) c_{2} \right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 96
DSolve[{x'[t]==-x[t]-2*y[t],y'[t]==2*x[t]-3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{3} e^{-2 t} \left (3 c_1 \cos \left (\sqrt {3} t\right )+\sqrt {3} (c_1-2 c_2) \sin \left (\sqrt {3} t\right )\right ) \\ y(t)\to \frac {1}{3} e^{-2 t} \left (3 c_2 \cos \left (\sqrt {3} t\right )+\sqrt {3} (2 c_1-c_2) \sin \left (\sqrt {3} t\right )\right ) \\ \end{align*}