90.5.21 problem 22

Internal problem ID [25140]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 71
Problem number : 22
Date solved : Thursday, October 02, 2025 at 11:53:51 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Maple. Time used: 0.010 (sec). Leaf size: 23

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

\[ y = t -2 \arctan \left (\frac {c_1 -t +2}{c_1 -t}\right ) \]

✓ Mathematica. Time used: 0.219 (sec). Leaf size: 64

ode=D[y[t],{t,1}] == Sin[t-y[t]]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [y(t)-\sec (t-y(t)) \left (2 \sqrt {\cos ^2(t-y(t))} \arcsin \left (\frac {\sqrt {1-\sin (t-y(t))}}{\sqrt {2}}\right )+\sin (t-y(t))+1\right )=c_1,y(t)\right ] \]

✓ Sympy. Time used: 1.045 (sec). Leaf size: 15

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

\[ y{\left (t \right )} = t - 2 \operatorname {atan}{\left (\frac {C_{1} + t - 2}{C_{1} + t} \right )} \]