Internal problem ID [10788]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 36.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {2 x +2 y-1+\left (x +y-2\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve((2*x+2*y(x)-1)+(x+y(x)-2)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -x -3 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {x}{3}} c_{1} {\mathrm e}^{-\frac {1}{3}}}{3}\right )-1 \]
✓ Solution by Mathematica
Time used: 3.875 (sec). Leaf size: 35
DSolve[(2*x+2*y[x]-1)+(x+y[x]-2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -3 W\left (-e^{\frac {x}{3}-1+c_1}\right )-x-1 \\ y(x)\to -x-1 \\ \end{align*}