75.8.19 problem 217

Internal problem ID [16764]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 8. First order not solved for the derivative. Exercises page 67
Problem number : 217
Date solved : Monday, March 31, 2025 at 03:16:26 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.056 (sec). Leaf size: 38

ode=x==D[y[x],x]+Sin[D[y[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)