88.4.9 problem 9

Internal problem ID [23973]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 33
Problem number : 9
Date solved : Thursday, October 02, 2025 at 09:48:17 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 53

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

\[ y = \frac {6 \sqrt {3}}{-2 \sqrt {3}\, \ln \left (x +1\right )+\sqrt {3}\, \ln \left (x^{2}-x +1\right )+6 \sqrt {3}\, c_1 +6 \arctan \left (\frac {\left (2 x -1\right ) \sqrt {3}}{3}\right )} \]

✓ Mathematica. Time used: 0.105 (sec). Leaf size: 53

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

\begin{align*} y(x)&\to \frac {6}{2 \sqrt {3} \arctan \left (\frac {2 x-1}{\sqrt {3}}\right )+\log \left (x^2-x+1\right )-2 \log (x+1)-6 c_1}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.194 (sec). Leaf size: 42

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

\[ y{\left (x \right )} = - \frac {6}{C_{1} + 2 \log {\left (x + 1 \right )} - \log {\left (x^{2} - x + 1 \right )} - 2 \sqrt {3} \operatorname {atan}{\left (\frac {\sqrt {3} \left (2 x - 1\right )}{3} \right )}} \]