42.4.7 problem Problem 3.8

Internal problem ID [8835]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.6 Summary and Problems. Page 218
Problem number : Problem 3.8
Date solved : Tuesday, September 30, 2025 at 05:53:11 PM
CAS classification : [[_homogeneous, `class D`]]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 20

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

\[ y = \operatorname {RootOf}\left (\textit {\_Z} \,\operatorname {Si}\left (\textit {\_Z} \right )+\textit {\_Z} c_1 +\textit {\_Z} x +\cos \left (\textit {\_Z} \right )\right ) x \]

✓ Mathematica. Time used: 0.106 (sec). Leaf size: 28

ode=(1/y[x]+Sec[y[x]/x])-x/y[x]^2*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*Derivative(y(x), x)/y(x)**2 + 1/cos(y(x)/x) + 1/y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out