20.1.2 problem 1.b

Internal problem ID [4242]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, section 7, page 37
Problem number : 1.b
Date solved : Tuesday, September 30, 2025 at 07:08:25 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

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

\[ y = \frac {x^{2}}{-2 x +c_1} \]

✓ Mathematica. Time used: 0.089 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to \frac {x^2}{-2 x+c_1}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.113 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = \frac {x^{2}}{C_{1} - 2 x} \]