23.1.430 problem 420

Internal problem ID [5037]
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 : 420
Date solved : Tuesday, September 30, 2025 at 11:28:24 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 27

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

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

✓ Mathematica. Time used: 0.055 (sec). Leaf size: 39

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

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

✓ Sympy. Time used: 0.188 (sec). Leaf size: 22

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

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