60.1.343 problem 344

Internal problem ID [10357]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 344
Date solved : Monday, January 27, 2025 at 07:30:27 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 60.148 (sec). Leaf size: 23

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

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