78.1.21 problem 2 (g)

Internal problem ID [18076]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 2 (g)
Date solved : Tuesday, January 28, 2025 at 11:25:32 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 48

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

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