84.14.11 problem 7.19

Internal problem ID [22168]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 7. Integrating factors. Supplementary problems
Problem number : 7.19
Date solved : Thursday, October 02, 2025 at 08:33:16 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.013 (sec). Leaf size: 16

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

\begin{align*} y &= 0 \\ y &= \operatorname {LambertW}\left (\frac {1}{x c_1}\right ) \\ \end{align*}

✓ Mathematica. Time used: 0.868 (sec). Leaf size: 24

ode=(x*y[x]^2)+(x^2*y[x]^2+x^2*y[x])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.197 (sec). Leaf size: 7

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

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