68.4.34 problem 34

Internal problem ID [17214]
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 : Thursday, October 02, 2025 at 01:54:59 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.049 (sec). Leaf size: 50

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

\[ y = \arctan \left (\frac {{\mathrm e}^{-4 \cos \left (t \right )} c_1^{2}-1}{{\mathrm e}^{-4 \cos \left (t \right )} c_1^{2}+1}, \frac {2 c_1}{{\mathrm e}^{-2 \cos \left (t \right )} c_1^{2}+{\mathrm e}^{2 \cos \left (t \right )}}\right ) \]

✓ Mathematica. Time used: 0.056 (sec). Leaf size: 50

ode=D[y[t],t]==Sin[t-y[t]]+Sin[t+y[t]]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 1.309 (sec). Leaf size: 42

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-sin(t - y(t)) - sin(t + y(t)) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \left [ y{\left (t \right )} = \pi - \operatorname {asin}{\left (\frac {C_{1} + e^{4 \cos {\left (t \right )}}}{C_{1} - e^{4 \cos {\left (t \right )}}} \right )}, \ y{\left (t \right )} = \operatorname {asin}{\left (\frac {C_{1} + e^{4 \cos {\left (t \right )}}}{C_{1} - e^{4 \cos {\left (t \right )}}} \right )}\right ] \]