23.1.483 problem 473

Internal problem ID [5090]
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 : 473
Date solved : Tuesday, September 30, 2025 at 11:34:52 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (1-4 x -2 y\right ) y^{\prime }+2 x +y&=0 \end{align*}

✓ Maple. Time used: 0.024 (sec). Leaf size: 23

ode:=(1-4*x-2*y(x))*diff(y(x),x)+2*x+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\operatorname {LambertW}\left (-2 \,{\mathrm e}^{4-25 x +25 c_1}\right )}{10}+\frac {2}{5}-2 x \]

✓ Mathematica. Time used: 2.043 (sec). Leaf size: 39

ode=(1-4*x-2*y[x])*D[y[x],x]+2*x+y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {1}{10} W\left (-e^{-25 x-1+c_1}\right )-2 x+\frac {2}{5}\\ y(x)&\to \frac {2}{5}-2 x \end{align*}

✓ Sympy. Time used: 0.622 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x + (-4*x - 2*y(x) + 1)*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - 2 x - \frac {W\left (C_{1} e^{4 - 25 x}\right )}{10} + \frac {2}{5} \]