Internal problem ID [12805]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 3. Linear Systems. Exercises section 3.5 page 327
Problem number: 24.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-3 x \left (t \right )-y\\ y^{\prime }&=4 x \left (t \right )+y \end {align*}
With initial conditions \[ [x \left (0\right ) = -1, y \left (0\right ) = 2] \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve([diff(x(t),t) = -3*x(t)-y(t), diff(y(t),t) = 4*x(t)+y(t), x(0) = -1, y(0) = 2],[x(t), y(t)], singsol=all)
\begin{align*} x \left (t \right ) = -{\mathrm e}^{-t} y \left (t \right ) = 2 \,{\mathrm e}^{-t} \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 22
DSolve[{x'[t]==-3*x[t]-y[t],y'[t]==4*x[t]+y[t]},{x[0]==-1,y[0]==2},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -e^{-t} y(t)\to 2 e^{-t} \end{align*}