78.1.22 problem 2 (h)

Internal problem ID [18077]
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 : Tuesday, January 28, 2025 at 11:25:33 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.001 (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: 0.005 (sec). Leaf size: 16

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

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