Internal problem ID [12773]
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 3.2. page 277
Problem number: 13 (b).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-4 x \left (t \right )+y\\ y^{\prime }&=2 x \left (t \right )-3 y \end {align*}
With initial conditions \[ [x \left (0\right ) = 2, y \left (0\right ) = 1] \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve([diff(x(t),t) = -4*x(t)+y(t), diff(y(t),t) = 2*x(t)-3*y(t), x(0) = 2, y(0) = 1],[x(t), y(t)], singsol=all)
\begin{align*} x \left (t \right ) = {\mathrm e}^{-5 t}+{\mathrm e}^{-2 t} y \left (t \right ) = -{\mathrm e}^{-5 t}+2 \,{\mathrm e}^{-2 t} \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 34
DSolve[{x'[t]==-4*x[t]+y[t],y'[t]==2*x[t]-3*y[t]},{x[0]==2,y[0]==1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-5 t}+e^{-2 t} y(t)\to e^{-5 t} \left (2 e^{3 t}-1\right ) \end{align*}