43.21.10 problem 4(b)

Internal problem ID [9026]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 5. Existence and uniqueness of solutions to first order equations. Page 190
Problem number : 4(b)
Date solved : Tuesday, September 30, 2025 at 06:01:44 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 15

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

\[ y = x \operatorname {LambertW}\left (\frac {{\mathrm e}^{-c_1}}{x}\right ) \]

✓ Mathematica. Time used: 0.985 (sec). Leaf size: 21

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

\begin{align*} y(x)&\to x W\left (\frac {e^{c_1}}{x}\right )\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.263 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = x W\left (\frac {C_{1}}{x}\right ) \]