44.1.23 problem 2(i)

Internal problem ID [9081]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS. Page 9
Problem number : 2(i)
Date solved : Tuesday, September 30, 2025 at 06:03:49 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 39

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

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

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 26

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

\begin{align*} y(x)&\to \int _1^x\frac {K[1]}{K[1]^3+1}dK[1]+c_1 \end{align*}

✓ Sympy. Time used: 0.136 (sec). Leaf size: 41

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

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