83.16.5 problem 3

Internal problem ID [22046]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Examination I. page 253
Problem number : 3
Date solved : Thursday, October 02, 2025 at 08:23:08 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} x y^{2}&=y-x y^{\prime } \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.094 (sec). Leaf size: 23

ode=x*y[x]^2==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: 0.113 (sec). Leaf size: 10

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

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