23.1.594 problem 587

Internal problem ID [5201]
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 : 587
Date solved : Tuesday, September 30, 2025 at 11:54:45 AM
CAS classification : [[_homogeneous, `class G`], _exact, _rational, _Bernoulli]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 36

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

\begin{align*} y &= \frac {\sqrt {x \left (-a x +c_1 \right )}}{x^{2}} \\ y &= -\frac {\sqrt {x \left (-a x +c_1 \right )}}{x^{2}} \\ \end{align*}

✓ Mathematica. Time used: 0.161 (sec). Leaf size: 44

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

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

✓ Sympy. Time used: 0.337 (sec). Leaf size: 29

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

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