Internal problem ID [5369]
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(e).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime }-\arctan \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve((1+x^2)*diff(y(x),x)=arctan(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\arctan \left (x \right )^{2}}{2}+c_{1} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 16
DSolve[(1+x^2)*y'[x]==ArcTan[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\arctan (x)^2}{2}+c_1 \\ \end{align*}