Internal problem ID [13118]
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: 7.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-2 x \left (t \right )-y\\ y^{\prime }&=x \left (t \right )-4 y \end {align*}
With initial conditions \[ [x \left (0\right ) = 1, y \left (0\right ) = 0] \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve([diff(x(t),t) = -2*x(t)-y(t), diff(y(t),t) = x(t)-4*y(t), x(0) = 1, y(0) = 0], singsol=all)
\begin{align*} x \left (t \right ) &= \left (t +1\right ) {\mathrm e}^{-3 t} \\ y \left (t \right ) &= t \,{\mathrm e}^{-3 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 24
DSolve[{x'[t]==-2*x[t]-1*y[t],y'[t]==1*x[t]-4*y[t]},{x[0]==1,y[0]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-3 t} (t+1) \\ y(t)\to e^{-3 t} t \\ \end{align*}