Internal problem ID [809]
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: 2 part 2.
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 \[ [x \relax (0) = 4, y \relax (0) = 0] \]
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 15
dsolve([diff(x(t),t) = -x(t), diff(y(t),t) = 2*y(t), x(0) = 4, y(0) = 0],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = 4 \,{\mathrm e}^{-t} \] \[ y \relax (t ) = 0 \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 16
DSolve[{x'[t]==-1*x[t]+0*y[t],y'[t]==0*x[t]+2*y[t]},{x[0]==4,y[0]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 4 e^{-t} \\ y(t)\to 0 \\ \end{align*}