9.2.9 problem 9

Internal problem ID [2879]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 6, page 25
Problem number : 9
Date solved : Tuesday, September 30, 2025 at 05:56:30 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} \left (x y-x^{2}\right ) y^{\prime }-y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 1.126 (sec). Leaf size: 25

ode=(x*y[x]-x^2)*D[y[x],x]-y[x]^2==0; 
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: 0.283 (sec). Leaf size: 10

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

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