Internal problem ID [15509]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 3 (Systems of differential equations). Section 20. The method of elimination.
Exercises page 212
Problem number: 778.
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*}
With initial conditions \[ [x \left (0\right ) = 1, y \left (0\right ) = 4] \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 32
dsolve([diff(x(t),t)+3*x(t)+4*y(t) = 0, diff(y(t),t)+2*x(t)+5*y(t) = 0, x(0) = 1, y(0) = 4], singsol=all)
\begin{align*} x \left (t \right ) &= 3 \,{\mathrm e}^{-7 t}-2 \,{\mathrm e}^{-t} \\ y \left (t \right ) &= 3 \,{\mathrm e}^{-7 t}+{\mathrm e}^{-t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 36
DSolve[{x'[t]+3*x[t]+4*y[t]==0,y'[t]+2*x[t]+5*y[t]==0},{x[0]==1,y[0]==4},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-7 t} \left (3-2 e^{6 t}\right ) \\ y(t)\to e^{-7 t} \left (e^{6 t}+3\right ) \\ \end{align*}