78.1.41 problem 4 (c)

Internal problem ID [18096]
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 : 4 (c)
Date solved : Tuesday, January 28, 2025 at 11:26:09 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.083 (sec). Leaf size: 11

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

\[ y = \ln \left (-\arctan \left (x \right )+1\right ) \]

✓ Solution by Mathematica

Time used: 0.393 (sec). Leaf size: 12

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

\[ y(x)\to \log (1-\arctan (x)) \]