23.1.568 problem 558

Internal problem ID [5175]
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 : 558
Date solved : Tuesday, September 30, 2025 at 11:49:56 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x \left (2 x +3 y\right ) y^{\prime }+3 \left (x +y\right )^{2}&=0 \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 63

ode:=x*(2*x+3*y(x))*diff(y(x),x)+3*(x+y(x))^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {-4 c_1 \,x^{2}-\sqrt {-2 x^{4} c_1^{2}+6}}{6 c_1 x} \\ y &= \frac {-4 c_1 \,x^{2}+\sqrt {-2 x^{4} c_1^{2}+6}}{6 c_1 x} \\ \end{align*}

✓ Mathematica. Time used: 0.916 (sec). Leaf size: 135

ode=x*(2*x+3*y[x])*D[y[x],x]+3*(x+y[x])^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {4 x^2+\sqrt {-2 x^4+6 e^{4 c_1}}}{6 x}\\ y(x)&\to \frac {-4 x^2+\sqrt {-2 x^4+6 e^{4 c_1}}}{6 x}\\ y(x)&\to -\frac {\sqrt {2} \sqrt {-x^4}+4 x^2}{6 x}\\ y(x)&\to \frac {\sqrt {2} \sqrt {-x^4}-4 x^2}{6 x} \end{align*}

✓ Sympy. Time used: 1.067 (sec). Leaf size: 42

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(2*x + 3*y(x))*Derivative(y(x), x) + 3*(x + y(x))**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \frac {2 x}{3} - \frac {\sqrt {C_{1} - 2 x^{4}}}{6 x}, \ y{\left (x \right )} = - \frac {2 x}{3} + \frac {\sqrt {C_{1} - 2 x^{4}}}{6 x}\right ] \]