50.1.19 problem 2(e)

Internal problem ID [7791]
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)
Date solved : Monday, January 27, 2025 at 03:23:17 PM
CAS classification : [_quadrature]

\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=\arctan \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 12

dsolve((1+x^2)*diff(y(x),x)=arctan(x),y(x), singsol=all)
 

\[ y = \frac {\arctan \left (x \right )^{2}}{2}+c_{1} \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 16

DSolve[(1+x^2)*D[y[x],x]==ArcTan[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\arctan (x)^2}{2}+c_1 \]