23.1.447 problem 437

Internal problem ID [5054]
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 : 437
Date solved : Tuesday, September 30, 2025 at 11:30:33 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 35

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

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

✓ Mathematica. Time used: 0.245 (sec). Leaf size: 84

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

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

✓ Sympy. Time used: 0.585 (sec). Leaf size: 26

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

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