Internal problem ID [7923]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 344.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
\[ \boxed {\left (-1+2 x +\ln \left (y\right )\right ) y^{\prime }-2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve((ln(y(x))+2*x-1)*diff(y(x),x)-2*y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\operatorname {LambertW}\left (-2 \,{\mathrm e}^{-2 x} c_{1} \right )-2 x} \]
✓ Solution by Mathematica
Time used: 60.141 (sec). Leaf size: 23
DSolve[-2*y[x] + (-1 + 2*x + Log[y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {W\left (-2 c_1 e^{-2 x}\right )}{2 c_1} \\ \end{align*}