Internal problem ID [10545]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY.
2015.
Section: Chapter 4, Linear Systems. Exercises page 237
Problem number: 5.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 x \left (t \right )+y \left (t \right )\\ y^{\prime }\left (t \right )&=-x \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 1, y \left (0\right ) = -1] \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 14
dsolve([diff(x(t),t) = 2*x(t)+y(t), diff(y(t),t) = -x(t), x(0) = 1, y(0) = -1],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = {\mathrm e}^{t} \] \[ y \left (t \right ) = -{\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 16
DSolve[{x'[t]==2*x[t]+y[t],y'[t]==-x[t]+0*y[t]},{x[0]==1,y[0]==-1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^t \\ y(t)\to -e^t \\ \end{align*}