Internal problem ID [12744]
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: 4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-x \left (t \right )+2 y\\ y^{\prime }&=2 x \left (t \right )-y \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve([diff(x(t),t)=-x(t)+2*y(t),diff(y(t),t)=2*x(t)-y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = c_{1} {\mathrm e}^{t}-c_{2} {\mathrm e}^{-3 t} \] \[ y \left (t \right ) = c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{-3 t} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 68
DSolve[{x'[t]==-x[t]+2*y[t],y'[t]==2*x[t]-y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} e^{-3 t} \left (c_1 \left (e^{4 t}+1\right )+c_2 \left (e^{4 t}-1\right )\right ) y(t)\to \frac {1}{2} e^{-3 t} \left (c_1 \left (e^{4 t}-1\right )+c_2 \left (e^{4 t}+1\right )\right ) \end{align*}