Internal problem ID [13092]
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 (a).
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 \[ [x \left (0\right ) = 1, y \left (0\right ) = 0] \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve([diff(x(t),t) = -4*x(t)+y(t), diff(y(t),t) = 2*x(t)-3*y(t), x(0) = 1, y(0) = 0], singsol=all)
\begin{align*} x \left (t \right ) &= \frac {2 \,{\mathrm e}^{-5 t}}{3}+\frac {{\mathrm e}^{-2 t}}{3} \\ y \left (t \right ) &= -\frac {2 \,{\mathrm e}^{-5 t}}{3}+\frac {2 \,{\mathrm e}^{-2 t}}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 40
DSolve[{x'[t]==-4*x[t]+y[t],y'[t]==2*x[t]-3*y[t]},{x[0]==1,y[0]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{3} e^{-5 t} \left (e^{3 t}+2\right ) \\ y(t)\to \frac {2}{3} e^{-5 t} \left (e^{3 t}-1\right ) \\ \end{align*}