Internal problem ID [7806]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 226.
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 (4 y-2 x -3\right ) y^{\prime }+2 y-x -1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.03 (sec). Leaf size: 21
dsolve((4*y(x)-2*x-3)*diff(y(x),x)+2*y(x)-x-1=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {x}{2}-\frac {\LambertW \left (-{\mathrm e}^{5} {\mathrm e}^{8 x} c_{1}\right )}{8}+\frac {5}{8} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 28
DSolve[(4*y[x]-2*x-3)*y'[x]+2*y[x]-x-1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{8} \left (-\operatorname {ProductLog}\left (-e^{8 x-1+c_1}\right )+4 x+5\right ) \\ \end{align*}