78.1.31 problem 2 (q)

Internal problem ID [18086]
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 (q)
Date solved : Tuesday, January 28, 2025 at 11:25:52 AM
CAS classification : [_separable]

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+1+y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 11

dsolve((1+x^2)*diff(y(x),x)+(1+y(x)^2)=0,y(x), singsol=all)
 

\[ y = -\tan \left (\arctan \left (x \right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.242 (sec). Leaf size: 29

DSolve[(1+x^2)*D[y[x],x]+(1+y[x]^2)==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\tan (\arctan (x)-c_1) \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}