Internal problem ID [14028]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 38. Systems of differential equations. A starting point. Additional Exercises.
page 786
Problem number: 38.10 (b).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 y \left (t \right )\\ y^{\prime }\left (t \right )&=2 x \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
dsolve([diff(x(t),t)=2*y(t),diff(y(t),t)=2*x(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{2 t}+c_{2} {\mathrm e}^{-2 t} \\ y \left (t \right ) &= c_{1} {\mathrm e}^{2 t}-c_{2} {\mathrm e}^{-2 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 68
DSolve[{x'[t]==2*y[t],y'[t]==2*x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} e^{-2 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^{-2 t} \left (c_1 \left (e^{4 t}-1\right )+c_2 \left (e^{4 t}+1\right )\right ) \\ \end{align*}