44.5.21 problem 7(c)

Internal problem ID [9177]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.7. Homogeneous Equations. Page 28
Problem number : 7(c)
Date solved : Tuesday, September 30, 2025 at 06:12:05 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 36

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

\[ y = \operatorname {RootOf}\left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a}^{2} \cos \left (\frac {1}{\textit {\_a}}\right )}{\textit {\_a}^{3} \cos \left (\frac {1}{\textit {\_a}}\right )+\textit {\_a} -1}d \textit {\_a} +\ln \left (x \right )+c_1 \right ) x \]

✓ Mathematica. Time used: 0.661 (sec). Leaf size: 49

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {\cos \left (\frac {1}{K[1]}\right ) K[1]^2}{\cos \left (\frac {1}{K[1]}\right ) K[1]^3+K[1]-1}dK[1]=-\log (x)+c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out