Internal problem ID [14192]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number: 34.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\sin \left (t -y\right )-\sin \left (y+t \right )=0} \]
✓ Solution by Maple
Time used: 0.219 (sec). Leaf size: 51
dsolve(diff(y(t),t)=sin(t-y(t))+sin(t+y(t)),y(t), singsol=all)
\[ y \left (t \right ) = \arctan \left (\frac {{\mathrm e}^{-4 \cos \left (t \right )} c_{1}^{2}-1}{{\mathrm e}^{-4 \cos \left (t \right )} c_{1}^{2}+1}, \frac {2 \,{\mathrm e}^{-2 \cos \left (t \right )} c_{1}}{{\mathrm e}^{-4 \cos \left (t \right )} c_{1}^{2}+1}\right ) \]
✓ Solution by Mathematica
Time used: 0.53 (sec). Leaf size: 38
DSolve[y'[t]==Sin[t-y[t]]+Sin[t+y[t]],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 2 \arctan \left (\tanh \left (\frac {1}{2} (-2 \cos (t)+c_1)\right )\right ) \\ y(t)\to -\frac {\pi }{2} \\ y(t)\to \frac {\pi }{2} \\ \end{align*}