Internal problem ID [7924]
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]]
Solve \begin {gather*} \boxed {\left (\ln \relax (y)+2 x -1\right ) y^{\prime }-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 19
dsolve((ln(y(x))+2*x-1)*diff(y(x),x)-2*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\LambertW \left (-2 c_{1} {\mathrm e}^{-2 x}\right )-2 x} \]
✓ Solution by Mathematica
Time used: 69.868 (sec). Leaf size: 37
DSolve[-2*y[x] + (-1 + 2*x + Log[y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\text {ProductLog}\left (-2 c_1 e^{-2 x}\right )}{2 c_1} \\ y(x)\to 0 \\ y(x)\to e^{-2 x} \\ \end{align*}