Internal problem ID [15510]
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: 779.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )+5 y \left (t \right )\\ y^{\prime }\left (t \right )&=-x \left (t \right )-3 y \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = -2, y \left (0\right ) = 1] \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 27
dsolve([diff(x(t),t) = x(t)+5*y(t), diff(y(t),t) = -x(t)-3*y(t), x(0) = -2, y(0) = 1], singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{-t} \left (\sin \left (t \right )-2 \cos \left (t \right )\right ) \\ y \left (t \right ) &= {\mathrm e}^{-t} \cos \left (t \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 20
DSolve[{x'[t]+3*x[t]+4*y[t]==0,y'[t]+2*x[t]+5*y[t]==0},{x[0]==-2,y[0]==1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -2 e^{-t} \\ y(t)\to e^{-t} \\ \end{align*}