Internal problem ID [1930]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 7, page 28
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-y+\left (-y+x -1\right ) y^{\prime }=-x -1} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 13
dsolve((x-y(x)+1)+(x-y(x)-1)*diff(y(x),x)=0,y(x), singsol=all)
\[ y = \operatorname {LambertW}\left ({\mathrm e}^{-2 x} c_{1} \right )+x \]
✓ Solution by Mathematica
Time used: 3.902 (sec). Leaf size: 24
DSolve[(x-y[x]+1)+(x-y[x]-1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+W\left (-e^{-2 x-1+c_1}\right ) y(x)\to x \end{align*}