87.4.6 problem 6

Internal problem ID [23272]
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 37
Problem number : 6
Date solved : Thursday, October 02, 2025 at 09:27:56 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{2} y^{\prime }+y \tan \left (x \right )&=\sin \left (x \right )^{3} \end{align*}

✗ Maple

ode:=y(x)^2*diff(y(x),x)+y(x)*tan(x) = sin(x)^3; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]^2*D[y[x],x]+y[x]*Tan[x]==Sin[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(y(x)**2*Derivative(y(x), x) + y(x)*tan(x) - sin(x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -(-y(x)*tan(x) + sin(x)**3)/y(x)**2 + Derivative(y(x), x) cannot