30.3.19 problem 20

Internal problem ID [7475]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.4, Exact equations. Exercises. page 64
Problem number : 20
Date solved : Tuesday, September 30, 2025 at 04:37:25 PM
CAS classification : [_exact]

\begin{align*} \frac {2}{\sqrt {-x^{2}+1}}+y \cos \left (x y\right )+\left (x \cos \left (x y\right )-\frac {1}{y^{{1}/{3}}}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 20

ode:=2/(-x^2+1)^(1/2)+y(x)*cos(x*y(x))+(x*cos(x*y(x))-1/y(x)^(1/3))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \sin \left (x y\right )+2 \arcsin \left (x \right )-\frac {3 y^{{2}/{3}}}{2}+c_1 = 0 \]

✗ Mathematica

ode=( 2/Sqrt[1-x^2] + y[x]*Cos[x*y[x]] )+( x*Cos[x*y[x]]- 1/y[x]^(1/3)  )*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*cos(x*y(x)) - 1/y(x)**(1/3))*Derivative(y(x), x) + y(x)*cos(x*y(x)) + 2/sqrt(1 - x**2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out