23.1.367 problem 352

Internal problem ID [4974]
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 : 352
Date solved : Tuesday, September 30, 2025 at 09:06:40 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Riccati]

\begin{align*} x^{3} y^{\prime }+20+x^{2} y \left (1-x^{2} y\right )&=0 \end{align*}

✓ Maple. Time used: 0.209 (sec). Leaf size: 26

ode:=x^3*diff(y(x),x)+20+x^2*y(x)*(1-x^2*y(x)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {5 x^{9}+4 c_1}{x^{2} \left (-x^{9}+c_1 \right )} \]

✓ Mathematica. Time used: 0.098 (sec). Leaf size: 36

ode=x^3*D[y[x],x]+20+x^2*y[x]*(1-x^2*y[x])==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {-5 x^9+4 c_1}{x^2 \left (x^9+c_1\right )}\\ y(x)&\to \frac {4}{x^2} \end{align*}

✓ Sympy. Time used: 0.212 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), x) + x**2*(-x**2*y(x) + 1)*y(x) + 20,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {4 C_{1} - 5 x^{9} - 4}{x^{2} \left (C_{1} + x^{9} - 1\right )} \]