87.1.10 problem 10

Internal problem ID [23222]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 9
Problem number : 10
Date solved : Thursday, October 02, 2025 at 09:24:34 PM
CAS classification : [NONE]

\begin{align*} y^{\prime \prime }-\tan \left (x \right ) y^{\prime }-\frac {\tan \left (x \right ) y}{x}&=\frac {y^{3}}{x^{3}} \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x)-diff(y(x),x)*tan(x)-tan(x)/x*y(x) = 1/x^3*y(x)^3; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],{x,2}]-Tan[x]*D[y[x],x]-Tan[x]/x*y[x]==1/x^3*y[x]^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-tan(x)*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - y(x)*tan(x)/x - y(x)**3/x**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - Derivative(y(x), (x, 2))/tan(x) + y(x)/x +