Internal problem ID [8557]
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`]]
\[ \boxed {\left (2 y+x +1\right ) y^{\prime }-2 y=x -1} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 21
dsolve((2*y(x)+x+1)*diff(y(x),x)-(2*y(x)+x-1)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x}{2}+\frac {2 \operatorname {LambertW}\left (\frac {c_{1} {\mathrm e}^{\frac {9 x}{4}-\frac {1}{4}}}{4}\right )}{3}+\frac {1}{6} \]
✓ Solution by Mathematica
Time used: 4.843 (sec). Leaf size: 43
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 W\left (-e^{\frac {9 x}{4}-1+c_1}\right )-3 x+1\right ) \\ y(x)\to \frac {1}{6} (1-3 x) \\ \end{align*}