74.4.34 problem 34

Internal problem ID [15927]
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
Date solved : Tuesday, January 28, 2025 at 08:23:00 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\sin \left (t -y\right )+\sin \left (t +y\right ) \end{align*}

✓ Solution by Maple

Time used: 0.444 (sec). Leaf size: 51

dsolve(diff(y(t),t)=sin(t-y(t))+sin(t+y(t)),y(t), singsol=all)
 

\[ y = \arctan \left (\frac {{\mathrm e}^{-4 \cos \left (t \right )} c_{1}^{2}-1}{{\mathrm e}^{-4 \cos \left (t \right )} c_{1}^{2}+1}, \frac {2 \,{\mathrm e}^{-2 \cos \left (t \right )} c_{1}}{{\mathrm e}^{-4 \cos \left (t \right )} c_{1}^{2}+1}\right ) \]

✓ Solution by Mathematica

Time used: 0.091 (sec). Leaf size: 50

DSolve[D[y[t],t]==Sin[t-y[t]]+Sin[t+y[t]],y[t],t,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [-y(t) \int _1^t0dK[1]+\int _1^t-\sec (y(t)) (\sin (K[1]-y(t))+\sin (K[1]+y(t)))dK[1]+\coth ^{-1}(\sin (y(t)))=c_1,y(t)\right ] \]