Internal problem ID [10195]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1863.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-3 x \left (t \right )-4 y \left (t \right )\\ y^{\prime }\left (t \right )&=-2 x \left (t \right )-5 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 35
dsolve({diff(x(t),t)+3*x(t)+4*y(t)=0,diff(y(t),t)+2*x(t)+5*y(t)=0},{x(t), y(t)}, singsol=all)
\[ x \left (t \right ) = {\mathrm e}^{-t} c_{1} +c_{2} {\mathrm e}^{-7 t} \] \[ y \left (t \right ) = -\frac {{\mathrm e}^{-t} c_{1}}{2}+c_{2} {\mathrm e}^{-7 t} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 72
DSolve[{x'[t]+3*x[t]+4*y[t]==0,y'[t]+2*x[t]+5*y[t]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{3} e^{-7 t} \left (c_1 \left (2 e^{6 t}+1\right )-2 c_2 \left (e^{6 t}-1\right )\right ) y(t)\to \frac {1}{3} e^{-7 t} \left (c_2 \left (e^{6 t}+2\right )-c_1 \left (e^{6 t}-1\right )\right ) \end{align*}