23.1.15 problem 2(e)

Internal problem ID [4105]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 2. First order equations. Exercises at page 14
Problem number : 2(e)
Date solved : Monday, January 27, 2025 at 08:08:56 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: 0.043 (sec). Leaf size: 11

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

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

✓ Solution by Mathematica

Time used: 0.392 (sec). Leaf size: 12

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

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