Internal problem ID [9442]
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 }\relax (t )&=-3 x \relax (t )-4 y \relax (t )\\ y^{\prime }\relax (t )&=-2 x \relax (t )-5 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.063 (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)
\[ x \relax (t ) = c_{1} {\mathrm e}^{-7 t}+c_{2} {\mathrm e}^{-t} \] \[ y \relax (t ) = c_{1} {\mathrm e}^{-7 t}-\frac {c_{2} {\mathrm e}^{-t}}{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 67
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 (2 (c_1-c_2) e^{6 t}+c_1+2 c_2\right ) \\ y(t)\to \frac {1}{3} e^{-7 t} \left ((c_2-c_1) e^{6 t}+c_1+2 c_2\right ) \\ \end{align*}