78.1.22 problem 2 (h)

Internal problem ID [18006]
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 (h)
Date solved : Monday, March 31, 2025 at 04:56:15 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: 0.005 (sec). Leaf size: 16

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

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

✓ Sympy. Time used: 0.306 (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)
 

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