Internal problem ID [11178]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 18.
Transformation of variables. Page 26
Problem number: Ex 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], [_Abel, `2nd type`, `class C`], _dAlembert]
\[ \boxed {y^{\prime } \left (x +y\right )=1} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve((x+y(x))*diff(y(x),x)-1=0,y(x), singsol=all)
\[ y \left (x \right ) = -\operatorname {LambertW}\left (-c_{1} {\mathrm e}^{-x -1}\right )-x -1 \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 24
DSolve[(x+y[x])*y'[x]-1==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -W\left (c_1 \left (-e^{-x-1}\right )\right )-x-1 \]