79.5.3 problem (c)

Internal problem ID [21095]
Book : Ordinary Differential Equations. By Wolfgang Walter. Graduate texts in Mathematics. Springer. NY. QA372.W224 1998
Section : Chapter 1. First order equations: Some integrable cases. Excercises IX at page 45
Problem number : (c)
Date solved : Thursday, October 02, 2025 at 07:08:10 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

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

\[ y = -\frac {2 x}{x^{2}-2 c_1} \]

✓ Mathematica. Time used: 0.085 (sec). Leaf size: 23

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

\begin{align*} y(x)&\to -\frac {2 x}{x^2-2 c_1}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.114 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = \frac {2 x}{C_{1} - x^{2}} \]