89.4.25 problem 26

Internal problem ID [24347]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 39
Problem number : 26
Date solved : Thursday, October 02, 2025 at 10:20:54 PM
CAS classification : [_rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

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

\[ y = \frac {x^{3}-x}{-\ln \left (x \right )+c_1} \]

✓ Mathematica. Time used: 0.129 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to \frac {x-x^3}{\log (x)+c_1}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.188 (sec). Leaf size: 14

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

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