Internal problem ID [4017]
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]
Solve \begin {gather*} \boxed {{\mathrm e}^{y} \left (y^{\prime }+1\right )-{\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 16
dsolve(exp(y(x))*(diff(y(x),x)+1)=exp(x),y(x), singsol=all)
\[ y \relax (x ) = x +\ln \left (\frac {{\mathrm e}^{-2 x} c_{1}}{2}+\frac {1}{2}\right ) \]
✓ Solution by Mathematica
Time used: 2.01 (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*}