84.14.12 problem 7.20

Internal problem ID [22169]
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 : 7.20
Date solved : Thursday, October 02, 2025 at 08:33:16 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 22

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

\begin{align*} y &= 0 \\ y &= \frac {c_1}{x} \\ y &= -\frac {c_1}{x} \\ \end{align*}

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 21

ode=(x*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 \frac {c_1}{x}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.110 (sec). Leaf size: 5

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

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