30.6.9 problem 10

Internal problem ID [7544]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Review problems. page 79
Problem number : 10
Date solved : Tuesday, September 30, 2025 at 04:45:16 PM
CAS classification : [_rational]

\begin{align*} 1+\frac {1}{1+x^{2}+4 x y+y^{2}}+\left (\frac {1}{\sqrt {y}}+\frac {1}{1+x^{2}+2 x y+y^{2}}\right ) y^{\prime }&=0 \end{align*}

✗ Maple

ode:=1+1/(1+x^2+4*x*y(x)+y(x)^2)+(1/y(x)^(1/2)+1/(1+x^2+2*x*y(x)+y(x)^2))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(1+1/(1+x^2+2*x*y[x]+2*x*y[x]+y[x]^2) )+( 1/Sqrt[y[x]] + 1/(1+x^2+2*x*y[x]+y[x]^2)  )*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((1/sqrt(y(x)) + 1/(x**2 + 2*x*y(x) + y(x)**2 + 1))*Derivative(y(x), x) + 1 + 1/(x**2 + 4*x*y(x) + y(x)**2 + 1),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out