32.6.4 problem Exercise 12.4, page 103

Internal problem ID [5869]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.4, page 103
Date solved : Monday, January 27, 2025 at 01:21:49 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.053 (sec). Leaf size: 19

dsolve(exp(y(x))*(diff(y(x),x)+1)=exp(x),y(x), singsol=all)
 

\[ y \left (x \right ) = x -\ln \left (2\right )+\ln \left (1+{\mathrm e}^{-2 x} c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 1.259 (sec). Leaf size: 22

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

\[ y(x)\to -x+\log \left (\frac {e^{2 x}}{2}+c_1\right ) \]