34.3.9 problem 23 (o)

Internal problem ID [7900]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 23 (o)
Date solved : Tuesday, September 30, 2025 at 05:09:37 PM
CAS classification : [_exact, _rational]

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

✓ Maple. Time used: 0.036 (sec). Leaf size: 69

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

\[ y = x \left (-1+{\mathrm e}^{-\operatorname {RootOf}\left (x^{3} {\mathrm e}^{2 \textit {\_Z}}+x^{2} {\mathrm e}^{2 \textit {\_Z}}-2 x^{3} {\mathrm e}^{\textit {\_Z}}+c_1 \,{\mathrm e}^{2 \textit {\_Z}}-\textit {\_Z} \,{\mathrm e}^{2 \textit {\_Z}}+2 x \,{\mathrm e}^{2 \textit {\_Z}}-2 x^{2} {\mathrm e}^{\textit {\_Z}}+x^{3}+x^{2}\right )}\right ) \]

✓ Mathematica. Time used: 0.331 (sec). Leaf size: 29

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

\[ \text {Solve}\left [x y(x)^2+y(x)^2+\log (y(x)+x)+2 x-\log (x)=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out