Internal problem ID [9439]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1864.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-5 x \left (t \right )-2 y \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right )-7 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 46
dsolve({diff(x(t),t)=-5*x(t)-2*y(t),diff(y(t),t)=x(t)-7*y(t)},{x(t), y(t)}, singsol=all)
\[ x \left (t \right ) = {\mathrm e}^{-6 t} \left (c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right )\right ) \] \[ y \left (t \right ) = \frac {{\mathrm e}^{-6 t} \left (c_{1} \sin \left (t \right )+\sin \left (t \right ) c_{2} -\cos \left (t \right ) c_{1} +c_{2} \cos \left (t \right )\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 52
DSolve[{x'[t]==-5*x[t]-2*y[t],y'[t]==x[t]-7*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-6 t} (c_1 \cos (t)+(c_1-2 c_2) \sin (t)) \\ y(t)\to e^{-6 t} (c_2 \cos (t)+(c_1-c_2) \sin (t)) \\ \end{align*}