50.1.23 problem 2(i)

Internal problem ID [7795]
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 : Monday, January 27, 2025 at 03:23:20 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 39

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

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

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 48

DSolve[(1+x^3)*D[y[x],x]==x,y[x],x,IncludeSingularSolutions -> True]
 

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