67.5.5 problem 6.3 (a)

Internal problem ID [16403]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number : 6.3 (a)
Date solved : Thursday, October 02, 2025 at 01:28:34 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

\[ y = \frac {x}{-\ln \left (x \right )+c_1} \]

✓ Mathematica. Time used: 0.083 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.113 (sec). Leaf size: 8

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

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