Internal problem ID [4016]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {{\mathrm e}^{y} \left (1+y^{\prime }\right )-{\mathrm e}^{x}=0} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 16
dsolve(exp(y(x))*(diff(y(x),x)+1)=exp(x),y(x), singsol=all)
\[ y \left (x \right ) = x +\ln \left (\frac {c_{1} {\mathrm e}^{-2 x}}{2}+\frac {1}{2}\right ) \]
✓ Solution by Mathematica
Time used: 1.335 (sec). Leaf size: 22
DSolve[Exp[y[x]]*(y'[x]+1)==Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x+\log \left (\frac {e^{2 x}}{2}+c_1\right ) \\ \end{align*}