Internal problem ID [9441]
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 }\relax (t )&=-y \relax (t )\\ y^{\prime }\relax (t )&=2 x \relax (t )+2 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.062 (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)
\[ x \relax (t ) = {\mathrm e}^{t} \left (c_{1} \sin \relax (t )+c_{2} \cos \relax (t )\right ) \] \[ y \relax (t ) = -{\mathrm e}^{t} \left (c_{1} \sin \relax (t )-\sin \relax (t ) c_{2}+\cos \relax (t ) c_{1}+c_{2} \cos \relax (t )\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (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*}