44.1.19 problem 2(e)

Internal problem ID [9077]
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 : Tuesday, September 30, 2025 at 06:03:47 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

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

\[ y = \frac {\arctan \left (x \right )^{2}}{2}+c_1 \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 16

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

\begin{align*} y(x)&\to \frac {\arctan (x)^2}{2}+c_1 \end{align*}

✓ Sympy. Time used: 0.197 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x**2 + 1)*Derivative(y(x), x) - atan(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + \frac {\operatorname {atan}^{2}{\left (x \right )}}{2} \]