23.1.481 problem 471

Internal problem ID [5088]
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 : 471
Date solved : Tuesday, September 30, 2025 at 11:34:47 AM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 51

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

\begin{align*} y &= -x -\frac {\sqrt {-3 x^{3}+9 x^{2}-9 c_1}}{3} \\ y &= -x +\frac {\sqrt {-3 x^{3}+9 x^{2}-9 c_1}}{3} \\ \end{align*}

✓ Mathematica. Time used: 0.087 (sec). Leaf size: 53

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

\begin{align*} y(x)&\to -x-\sqrt {-\frac {x^3}{3}+x^2+c_1}\\ y(x)&\to -x+\sqrt {-\frac {x^3}{3}+x^2+c_1} \end{align*}

✓ Sympy. Time used: 1.599 (sec). Leaf size: 42

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

\[ \left [ y{\left (x \right )} = - x - \frac {\sqrt {C_{1} - 3 x^{3} + 9 x^{2}}}{3}, \ y{\left (x \right )} = - x + \frac {\sqrt {C_{1} - 3 x^{3} + 9 x^{2}}}{3}\right ] \]