29.26.9 problem 745

Internal problem ID [5330]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 26
Problem number : 745
Date solved : Monday, January 27, 2025 at 11:14:53 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} \left (1-2 x -\ln \left (y\right )\right ) y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 60.154 (sec). Leaf size: 23

DSolve[(1-2*x -Log[y[x]])*D[y[x],x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {W\left (-2 c_1 e^{-2 x}\right )}{2 c_1} \]