Internal problem ID [14929]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 6. Systems of Differential Equations. Exercises 6.1, page 282
Problem number: 12.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=y \left (t \right )\\ y^{\prime }\left (t \right )&=-x+2 \cos \left (t \right ) \sin \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 39
dsolve([diff(x(t),t)=y(t),diff(y(t),t)=-x(t)+sin(2*t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} \sin \left (t \right )+c_{1} \cos \left (t \right )-\frac {\sin \left (2 t \right )}{3} \\ y \left (t \right ) &= c_{2} \cos \left (t \right )-c_{1} \sin \left (t \right )-\frac {2 \cos \left (2 t \right )}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 46
DSolve[{x'[t]==y[t],y'[t]==-x[t]+Sin[2*t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_2 \sin (t)+\cos (t) \left (-\frac {2 \sin (t)}{3}+c_1\right ) \\ y(t)\to -\frac {2}{3} \cos (2 t)+c_2 \cos (t)-c_1 \sin (t) \\ \end{align*}