Internal problem ID [13071]
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: 25.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )-y\\ y^{\prime }&=x \left (t \right )+3 y \end {align*}
With initial conditions \[ [x \left (0\right ) = 0, y \left (0\right ) = 2] \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve([diff(x(t),t) = x(t)-y(t), diff(y(t),t) = x(t)+3*y(t), x(0) = 0, y(0) = 2], singsol=all)
\begin{align*} x \left (t \right ) &= -2 \,{\mathrm e}^{2 t} t \\ y \left (t \right ) &= -{\mathrm e}^{2 t} \left (-2 t -2\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 26
DSolve[{x'[t]==x[t]-y[t],y'[t]==x[t]+3*y[t]},{x[0]==0,y[0]==2},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -2 e^{2 t} t \\ y(t)\to 2 e^{2 t} (t+1) \\ \end{align*}