21.1.3 problem 3

Internal problem ID [4079]
Book : Differential equations, Shepley L. Ross, 1964
Section : 2.4, page 55
Problem number : 3
Date solved : Sunday, March 30, 2025 at 02:16:32 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

Timed Out