Internal problem ID [3938]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 8
Problem number: Differential equations with Linear Coefficients. Exercise 8.6, page
69.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {x +y+\left (2 x +2 y-1\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.033 (sec). Leaf size: 29
dsolve((x+y(x))+(2*x+2*y(x)-1)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\LambertW \left (2 \,{\mathrm e}^{x} {\mathrm e}^{-2} {\mathrm e}^{-c_{1}}\right )+x -2-c_{1}}-x +1 \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 24
DSolve[(x+y[x])+(2*x+2*y[x]-1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (\text {ProductLog}\left (-e^{x-1+c_1}\right )-2 x+2\right ) \\ \end{align*}