50.2.10 problem 1(j)

Internal problem ID [7816]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.3 SEPARABLE EQUATIONS. Page 12
Problem number : 1(j)
Date solved : Wednesday, March 05, 2025 at 05:06:55 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 12

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

\[ y = \frac {1}{-\ln \left (x \right )+c_{1}} \]

✓ Mathematica. Time used: 0.11 (sec). Leaf size: 19

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

\begin{align*} y(x)\to -\frac {1}{\log (x)+c_1} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.160 (sec). Leaf size: 10

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

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