Internal problem ID [7804]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 224.
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-6 x \right ) y^{\prime }-y+3 x +2=0} \end {gather*}
✓ Solution by Maple
Time used: 0.03 (sec). Leaf size: 35
dsolve((2*y(x)-6*x)*diff(y(x),x)-y(x)+3*x+2=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{-\LambertW \left (-\frac {{\mathrm e}^{\frac {25 x}{4}} {\mathrm e}^{-1} {\mathrm e}^{-\frac {25 c_{1}}{4}}}{2}\right )+\frac {25 x}{4}-1-\frac {25 c_{1}}{4}}}{5}+3 x -\frac {2}{5} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 29
DSolve[(2*y[x]-6*x)*y'[x]-y[x]+3*x+2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 3 x-\frac {2}{5} \left (1+\operatorname {ProductLog}\left (-e^{\frac {25 x}{4}-1+c_1}\right )\right ) \\ \end{align*}