Internal problem ID [9437]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1862.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-y \left (t \right )\\ y^{\prime }\left (t \right )&=2 x \left (t \right )+2 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 42
dsolve({diff(x(t),t)=-y(t),diff(y(t),t)=2*x(t)+2*y(t)},{x(t), y(t)}, singsol=all)
\[ x \left (t \right ) = {\mathrm e}^{t} \left (c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right )\right ) \] \[ y \left (t \right ) = -{\mathrm e}^{t} \left (c_{1} \sin \left (t \right )-\sin \left (t \right ) c_{2} +\cos \left (t \right ) c_{1} +c_{2} \cos \left (t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 46
DSolve[{x'[t]==-y[t],y'[t]==2*x[t]+2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^t (c_1 \cos (t)-(c_1+c_2) \sin (t)) \\ y(t)\to e^t (2 c_1 \sin (t)+c_2 (\sin (t)+\cos (t))) \\ \end{align*}