56.1.58 problem 58

Internal problem ID [8770]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 58
Date solved : Wednesday, March 05, 2025 at 06:46:21 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=-4 \sin \left (-y+x \right )-4 \end{align*}

✓ Maple. Time used: 0.030 (sec). Leaf size: 21

ode:=diff(y(x),x) = -4*sin(x-y(x))-4; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x +2 \arctan \left (\frac {3 \tan \left (-\frac {3 x}{2}+\frac {3 c_{1}}{2}\right )}{5}+\frac {4}{5}\right ) \]

✗ Mathematica

ode=D[y[x],x]==4*Sin[y[x]-x]-4; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✓ Sympy. Time used: 4.755 (sec). Leaf size: 42

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*sin(x - y(x)) + Derivative(y(x), x) + 4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ C_{1} + x - \frac {2 \operatorname {atan}{\left (\frac {5 \tan {\left (\frac {x}{2} - \frac {y{\left (x \right )}}{2} \right )}}{3} + \frac {4}{3} \right )}}{3} - \frac {2 \pi \left \lfloor {\frac {x - y{\left (x \right )} - \pi }{2 \pi }}\right \rfloor }{3} = 0 \]