23.1.368 problem 353

Internal problem ID [4975]
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 : 353
Date solved : Tuesday, September 30, 2025 at 09:06:42 AM
CAS classification : [_rational, _Riccati]

\begin{align*} x^{3} y^{\prime }+3+\left (3-2 x \right ) x^{2} y-x^{6} y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 27

ode:=x^3*diff(y(x),x)+3+(3-2*x)*x^2*y(x)-x^6*y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-3 \,{\mathrm e}^{4 x} c_1 -3}{x^{3} \left ({\mathrm e}^{4 x} c_1 -3\right )} \]

✓ Mathematica. Time used: 0.115 (sec). Leaf size: 34

ode=x^3*D[y[x],x]+3+(3-2*x)*x^2*y[x]-x^6*y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {-3+\frac {1}{\frac {1}{4}+c_1 e^{4 x}}}{x^3}\\ y(x)&\to -\frac {3}{x^3} \end{align*}

✓ Sympy. Time used: 0.215 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**6*y(x)**2 + x**3*Derivative(y(x), x) + x**2*(3 - 2*x)*y(x) + 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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