60.1.337 problem 344

Internal problem ID [10351]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 344
Date solved : Sunday, March 30, 2025 at 04:23:00 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*}

✓ Maple. Time used: 0.030 (sec). Leaf size: 17

ode:=(ln(y(x))+2*x-1)*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: 60.148 (sec). Leaf size: 23

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

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

✓ Sympy. Time used: 0.660 (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)
 

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