Internal problem ID [14044]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 39. Critical points, Direction fields and trajectories. Additional Exercises. page
815
Problem number: 39.2.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-x \left (t \right )+2 y \left (t \right )\\ y^{\prime }\left (t \right )&=2 x \left (t \right )-y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve([diff(x(t),t)=-x(t)+2*y(t),diff(y(t),t)=2*x(t)-y(t)],singsol=all)
\begin{align*} 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} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.007 (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*}