Internal problem ID [12541]
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: 5.
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 )-y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 46
dsolve([diff(x(t),t)=-x(t)+2*y(t),diff(y(t),t)=-2*x(t)-1*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -{\mathrm e}^{-t} \left (\cos \left (2 t \right ) c_{1} -\sin \left (2 t \right ) c_{2} \right ) \] \[ y \left (t \right ) = {\mathrm e}^{-t} \left (\cos \left (2 t \right ) c_{2} +\sin \left (2 t \right ) c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 51
DSolve[{x'[t]==-x[t]+2*y[t],y'[t]==-2*x[t]-1*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-t} (c_1 \cos (2 t)+c_2 \sin (2 t)) y(t)\to e^{-t} (c_2 \cos (2 t)-c_1 \sin (2 t)) \end{align*}