Internal problem ID [7801]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 221.
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 {\left (2 y+x +1\right ) y^{\prime }-2 y-x +1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 21
dsolve((2*y(x)+x+1)*diff(y(x),x)-(2*y(x)+x-1)=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {x}{2}+\frac {2 \LambertW \left (\frac {{\mathrm e}^{-\frac {1}{4}} {\mathrm e}^{\frac {9 x}{4}} c_{1}}{4}\right )}{3}+\frac {1}{6} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 30
DSolve[(2*y[x]+x+1)*y'[x]-(2*y[x]+x-1)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} \left (4 \operatorname {ProductLog}\left (-e^{\frac {9 x}{4}-1+c_1}\right )-3 x+1\right ) \\ \end{align*}