83.43.17 problem Ex 18 page 23

Internal problem ID [19454]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter II. Equations of first order and first degree
Problem number : Ex 18 page 23
Date solved : Monday, March 31, 2025 at 07:17:40 PM
CAS classification : [`y=_G(x,y')`]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

Timed Out