23.2.344 problem 392

Internal problem ID [5699]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 392
Date solved : Tuesday, September 30, 2025 at 02:00:25 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 16

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

\[ y = \int \operatorname {RootOf}\left (\sin \left (\textit {\_Z} \right )+\textit {\_Z} -x \right )d x +c_1 \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 38

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

\[ \text {Solve}\left [\left \{x=K[1]+\sin (K[1]),y(x)=\int _1^{K[1]}(\cos (K[1]) K[1]+K[1])dK[1]+c_1\right \},\{y(x),K[1]\}\right ] \]

✗ Sympy

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

NotImplementedError : multiple generators [_X0, sin(_X0)] 
No algorithms are implemented to solve equation _X0 - x + sin(_X0)