23.1.599 problem 592

Internal problem ID [5206]
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 : 592
Date solved : Tuesday, September 30, 2025 at 11:55:05 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} 3 x^{4} y y^{\prime }&=1-2 x^{3} y^{2} \end{align*}

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

ode:=3*x^4*y(x)*diff(y(x),x) = 1-2*x^3*y(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {\sqrt {5}\, \sqrt {x^{{17}/{3}} \left (-2+5 c_1 \,x^{{5}/{3}}\right )}}{5 x^{{13}/{3}}} \\ y &= \frac {\sqrt {5}\, \sqrt {x^{{17}/{3}} \left (-2+5 c_1 \,x^{{5}/{3}}\right )}}{5 x^{{13}/{3}}} \\ \end{align*}

✓ Mathematica. Time used: 3.571 (sec). Leaf size: 51

ode=3*x^4*y[x]*D[y[x],x]==1-2*x^3*y[x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt {-\frac {2}{5 x^3}+\frac {c_1}{x^{4/3}}}\\ y(x)&\to \sqrt {-\frac {2}{5 x^3}+\frac {c_1}{x^{4/3}}} \end{align*}

✓ Sympy. Time used: 0.339 (sec). Leaf size: 49

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x**4*y(x)*Derivative(y(x), x) + 2*x**3*y(x)**2 - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \frac {\sqrt {5} \sqrt {\frac {C_{1}}{x^{\frac {4}{3}}} - \frac {2}{x^{3}}}}{5}, \ y{\left (x \right )} = \frac {\sqrt {5} \sqrt {\frac {C_{1}}{x^{\frac {4}{3}}} - \frac {2}{x^{3}}}}{5}\right ] \]