69.1.8 problem 9

Internal problem ID [17958]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 1. Basic concepts and definitions. Exercises page 18
Problem number : 9
Date solved : Thursday, October 02, 2025 at 02:31:26 PM
CAS classification : [`y=_G(x,y')`]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

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