82.6.3 problem 33-2

Internal problem ID [21850]
Book : The Differential Equations Problem Solver. VOL. II. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 33. Systems of ordinary differential equations. Page 1059
Problem number : 33-2
Date solved : Thursday, October 02, 2025 at 08:02:54 PM
CAS classification : [NONE]

\begin{align*} y^{\prime \prime } \cos \left (y\right )+\left (\cos \left (y\right )-y^{\prime } \sin \left (y\right )\right ) y^{\prime }-2 y x&=0 \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x)*cos(y(x))+(cos(y(x))-diff(y(x),x)*sin(y(x)))*diff(y(x),x)-2*x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],{x,2}]*Cos[y[x]]+(Cos[y[x]]-D[y[x],x]*Sin[y[x]])*D[y[x],x]-2*x*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x*y(x) + (-sin(y(x))*Derivative(y(x), x) + cos(y(x)))*Derivative(y(x), x) + cos(y(x))*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -(sqrt(-8*x*y(x)*sin(y(x)) + 2*sin(2*y(x))*Derivative(y(x), (x, 2)) + cos(y(x))**2) + cos(y(x)))/(2*sin(y(x))) + Derivative(y(x), x) cannot be solved by the factorable group method