54.1.99 problem 101

Internal problem ID [11413]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 101
Date solved : Tuesday, September 30, 2025 at 08:15:57 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} x y^{\prime }+x y^{2}-y&=0 \end{align*}

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

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

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

✓ Mathematica. Time used: 0.089 (sec). Leaf size: 23

ode=x*D[y[x],x] + x*y[x]^2 - y[x]==0; 
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)
 

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