25.2.2 problem 2

Internal problem ID [6858]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 3
Problem number : 2
Date solved : Tuesday, September 30, 2025 at 03:56:05 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _Bernoulli]

\begin{align*} 1+\frac {y^{2}}{x^{2}}-\frac {2 y y^{\prime }}{x}&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=1+y(x)^2/x^2-2*y(x)/x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.132 (sec). Leaf size: 38

ode=(1+y[x]^2/x^2)-2*y[x]/x*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.248 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(1 - 2*y(x)*Derivative(y(x), x)/x + y(x)**2/x**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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