Internal problem ID [11551]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 4, Linear Systems. Exercises page 202
Problem number: 1(c).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=-2 x\\ y^{\prime }\left (t \right )&=x \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 23
dsolve([diff(x(t),t)=-2*x(t),diff(y(t),t)=x(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -2 c_{2} {\mathrm e}^{-2 t} \] \[ y \left (t \right ) = c_{1} +c_{2} {\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 35
DSolve[{x'[t]==-2*x[t],y'[t]==x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^{-2 t} y(t)\to c_1 \left (\frac {1}{2}-\frac {e^{-2 t}}{2}\right )+c_2 \end{align*}