23.1.591 problem 584

Internal problem ID [5198]
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 : 584
Date solved : Tuesday, September 30, 2025 at 11:54:33 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} 3 x^{2} y y^{\prime }+1+2 x y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 42

ode:=3*x^2*y(x)*diff(y(x),x)+1+2*x*y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {\sqrt {x^{{10}/{3}} \left (-2 x^{{1}/{3}}+c_1 \right )}}{x^{{7}/{3}}} \\ y &= -\frac {\sqrt {x^{{10}/{3}} \left (-2 x^{{1}/{3}}+c_1 \right )}}{x^{{7}/{3}}} \\ \end{align*}

✓ Mathematica. Time used: 3.593 (sec). Leaf size: 47

ode=3*x^2*y[x]*D[y[x],x]+1+2*x*y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt {-\frac {2}{x}+\frac {c_1}{x^{4/3}}}\\ y(x)&\to \sqrt {-\frac {2}{x}+\frac {c_1}{x^{4/3}}} \end{align*}

✓ Sympy. Time used: 0.290 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x**2*y(x)*Derivative(y(x), x) + 2*x*y(x)**2 + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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