Internal problem ID [807]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 9.2, Autonomous Systems and Stability. page 517
Problem number: 1.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=-x \relax (t )\\ y^{\prime }\relax (t )&=-2 y \relax (t ) \end {align*}
With initial conditions \[ [x \relax (0) = 4, y \relax (0) = 2] \]
✓ Solution by Maple
Time used: 0.024 (sec). Leaf size: 20
dsolve([diff(x(t),t) = -x(t), diff(y(t),t) = -2*y(t), x(0) = 4, y(0) = 2],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = 4 \,{\mathrm e}^{-t} \] \[ y \relax (t ) = 2 \,{\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 22
DSolve[{x'[t]==-1*x[t]+0*y[t],y'[t]==-2*y[t]},{x[0]==4,y[0]==2},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 4 e^{-t} \\ y(t)\to 2 e^{-2 t} \\ \end{align*}