Internal problem ID [14021]
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: 38.1.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 y \left (t \right )\\ y^{\prime }\left (t \right )&=1-2 x \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 36
dsolve([diff(x(t),t)=2*y(t),diff(y(t),t)=1-2*x(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} \sin \left (2 t \right )+c_{1} \cos \left (2 t \right )+\frac {1}{2} \\ y \left (t \right ) &= c_{2} \cos \left (2 t \right )-c_{1} \sin \left (2 t \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 42
DSolve[{x'[t]==2*y[t],y'[t]==1-2*x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 \cos (2 t)+c_2 \sin (2 t)+\frac {1}{2} \\ y(t)\to c_2 \cos (2 t)-c_1 \sin (2 t) \\ \end{align*}