Internal problem ID [5374]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (x^{3}+1\right ) y^{\prime }-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 39
dsolve((1+x^3)*diff(y(x),x)=x,y(x), singsol=all)
\[ y \relax (x ) = -\frac {\ln \left (x +1\right )}{3}+\frac {\ln \left (x^{2}-x +1\right )}{6}+\frac {\sqrt {3}\, \arctan \left (\frac {\left (2 x -1\right ) \sqrt {3}}{3}\right )}{3}+c_{1} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 47
DSolve[(1+x^3)*y'[x]==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} \left (2 \sqrt {3} \text {ArcTan}\left (\frac {2 x-1}{\sqrt {3}}\right )-2 \log (x+1)+\log ((x-1) x+1)+6 c_1\right ) \\ \end{align*}