56.3.3 problem Ex 3

Internal problem ID [14090]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 10. Homogeneous equations. Page 15
Problem number : Ex 3
Date solved : Thursday, October 02, 2025 at 09:11:42 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.091 (sec). Leaf size: 19

ode=(y[x]^2-x*y[x])+x^2*D[y[x],x]==0; 
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)
 

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