25.3.6 problem 5.4

Internal problem ID [6871]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 4
Problem number : 5.4
Date solved : Tuesday, September 30, 2025 at 03:59:01 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{2}+\left (x y+x^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.017 (sec). Leaf size: 45

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

\begin{align*} y &= \frac {1+\sqrt {c_1 \,x^{2}+1}}{c_1 x} \\ y &= \frac {1-\sqrt {c_1 \,x^{2}+1}}{c_1 x} \\ \end{align*}

✓ Mathematica. Time used: 1.456 (sec). Leaf size: 80

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 {e^{2 c_1}-\sqrt {e^{2 c_1} \left (x^2+e^{2 c_1}\right )}}{x}\\ y(x)&\to \frac {\sqrt {e^{2 c_1} \left (x^2+e^{2 c_1}\right )}+e^{2 c_1}}{x}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 1.233 (sec). Leaf size: 31

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

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