23.1.746 problem 749

Internal problem ID [5353]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 749
Date solved : Tuesday, September 30, 2025 at 12:35:19 PM
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*}

✓ Maple. Time used: 0.088 (sec). Leaf size: 17

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

\[ y = -\frac {\operatorname {LambertW}\left (-2 c_1 \,{\mathrm e}^{-2 x}\right )}{2 c_1} \]

✓ Mathematica. Time used: 60.109 (sec). Leaf size: 23

ode=(1-2*x -Log[y[x]])*D[y[x],x]+2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.412 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-2*x - log(y(x)) + 1)*Derivative(y(x), x) + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {W\left (2 C_{1} e^{- 2 x}\right )}{2 C_{1}} \]