80.3.28 problem 29

Internal problem ID [21192]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 3. First order nonlinear differential equations. Excercise 3.7 at page 67
Problem number : 29
Date solved : Thursday, October 02, 2025 at 07:16:41 PM
CAS classification : [_rational]

\begin{align*} x^{2}+y^{2}+\left (a x y+y^{4}\right ) y^{\prime }&=0 \end{align*}

✗ Maple

ode:=x^2+y(x)^2+(a*x*y(x)+y(x)^4)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(x^2+y[x]^2)+(a*x*y[x]+y[x]^4)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(x**2 + (a*x*y(x) + y(x)**4)*Derivative(y(x), x) + y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out