9.4.19 problem 20

Internal problem ID [2932]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 8, page 34
Problem number : 20
Date solved : Tuesday, September 30, 2025 at 06:10:33 AM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 18

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

\[ y = -\frac {x}{\arcsin \left (\frac {\sin \left (x \right )+c_1}{x}\right )} \]

✓ Mathematica. Time used: 14.922 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to -\frac {x}{\arcsin \left (\frac {\sin (x)+c_1}{x}\right )}\\ y(x)&\to 0 \end{align*}

✗ Sympy

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

Timed Out