26.9 problem 745

Internal problem ID [3478]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 26
Problem number: 745.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]

Solve \begin {gather*} \boxed {\left (1-2 x -\ln \relax (y)\right ) y^{\prime }+2 y=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 19

dsolve((1-2*x-ln(y(x)))*diff(y(x),x)+2*y(x) = 0,y(x), singsol=all)
 

\[ y \relax (x ) = {\mathrm e}^{-\LambertW \left (-2 \,{\mathrm e}^{-2 x} c_{1}\right )-2 x} \]

Solution by Mathematica

Time used: 60.146 (sec). Leaf size: 23

DSolve[(1-2 x -Log[y[x]])y'[x]+2 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} \\ \end{align*}