23.1.520 problem 510

Internal problem ID [5127]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 510
Date solved : Tuesday, September 30, 2025 at 11:43:30 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 39

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

\begin{align*} y &= -\frac {\sqrt {-2 x^{4}+4 c_1}}{2 x} \\ y &= \frac {\sqrt {-2 x^{4}+4 c_1}}{2 x} \\ \end{align*}

✓ Mathematica. Time used: 0.128 (sec). Leaf size: 46

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

\begin{align*} y(x)&\to -\frac {\sqrt {-\frac {x^4}{2}+c_1}}{x}\\ y(x)&\to \frac {\sqrt {-\frac {x^4}{2}+c_1}}{x} \end{align*}

✓ Sympy. Time used: 0.248 (sec). Leaf size: 32

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)
 

\[ \left [ y{\left (x \right )} = - \frac {\sqrt {C_{1} - 2 x^{4}}}{2 x}, \ y{\left (x \right )} = \frac {\sqrt {C_{1} - 2 x^{4}}}{2 x}\right ] \]