29.8.2 problem 207

Internal problem ID [4807]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 207
Date solved : Sunday, March 30, 2025 at 03:59:09 AM
CAS classification : [`y=_G(x,y')`]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - sin(x - y(x))/x cannot be solved by the factorable group method