Internal problem ID [13070]
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 3.1. page 258
Problem number: 24.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 y\\ y^{\prime }&=x \left (t \right )+y \end {align*}
With initial conditions \[ [x \left (0\right ) = -2, y \left (0\right ) = -1] \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve([diff(x(t),t) = 2*y(t), diff(y(t),t) = x(t)+y(t), x(0) = -2, y(0) = -1], singsol=all)
\begin{align*} x \left (t \right ) &= -\frac {2 \,{\mathrm e}^{-t}}{3}-\frac {4 \,{\mathrm e}^{2 t}}{3} \\ y \left (t \right ) &= \frac {{\mathrm e}^{-t}}{3}-\frac {4 \,{\mathrm e}^{2 t}}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 44
DSolve[{x'[t]==2*y[t],y'[t]==x[t]+y[t]},{x[0]==-2,y[0]==-1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\frac {2}{3} e^{-t} \left (2 e^{3 t}+1\right ) \\ y(t)\to \frac {1}{3} e^{-t} \left (1-4 e^{3 t}\right ) \\ \end{align*}