88.3.4 problem 4

Internal problem ID [23958]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 1. Introduction. Exercise at page 22
Problem number : 4
Date solved : Thursday, October 02, 2025 at 09:47:42 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

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

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

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

✓ Mathematica. Time used: 0.082 (sec). Leaf size: 23

ode=D[y[x],x]-y[x]/x==y[x]^2; 
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: 0.170 (sec). Leaf size: 10

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

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