84.5.10 problem 3.3 (b)

Internal problem ID [22097]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 3. Classification of first-order differential equations. Solved problems. Page 11
Problem number : 3.3 (b)
Date solved : Thursday, October 02, 2025 at 08:24:45 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

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

\begin{align*} y &= 0 \\ y &= \ln \left (x \right )+c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 15

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

\begin{align*} y(x)&\to 0\\ y(x)&\to \log (x)+c_1 \end{align*}

✓ Sympy. Time used: 0.155 (sec). Leaf size: 10

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

\[ \left [ y{\left (x \right )} = 0, \ y{\left (x \right )} = C_{1} + \log {\left (x \right )}\right ] \]