23.1.506 problem 496

Internal problem ID [5113]
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 : 496
Date solved : Tuesday, September 30, 2025 at 11:39:36 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 3 \left (x +2 y\right ) y^{\prime }&=1-x -2 y \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 23

ode:=3*(x+2*y(x))*diff(y(x),x) = 1-x-2*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\operatorname {LambertW}\left (-{\mathrm e}^{-1-\frac {x}{6}+\frac {c_1}{6}}\right )-1-\frac {x}{2} \]

✓ Mathematica. Time used: 2.264 (sec). Leaf size: 39

ode=3*(x+2*y[x])*D[y[x],x]==1-x-2*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -W\left (-e^{-\frac {x}{6}-1+c_1}\right )-\frac {x}{2}-1\\ y(x)&\to -\frac {x}{2}-1 \end{align*}

✓ Sympy. Time used: 5.735 (sec). Leaf size: 178

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x + (3*x + 6*y(x))*Derivative(y(x), x) + 2*y(x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \frac {x}{2} - W\left (- \frac {\sqrt [6]{C_{1} e^{- x}}}{e}\right ) - 1, \ y{\left (x \right )} = - \frac {x}{2} - W\left (\frac {\sqrt [6]{C_{1} e^{- x}}}{e}\right ) - 1, \ y{\left (x \right )} = - \frac {x}{2} - W\left (- \frac {\sqrt [6]{C_{1} e^{- x}} \left (1 - \sqrt {3} i\right )}{2 e}\right ) - 1, \ y{\left (x \right )} = - \frac {x}{2} - W\left (\frac {\sqrt [6]{C_{1} e^{- x}} \left (1 - \sqrt {3} i\right )}{2 e}\right ) - 1, \ y{\left (x \right )} = - \frac {x}{2} - W\left (- \frac {\sqrt [6]{C_{1} e^{- x}} \left (1 + \sqrt {3} i\right )}{2 e}\right ) - 1, \ y{\left (x \right )} = - \frac {x}{2} - W\left (\frac {\sqrt [6]{C_{1} e^{- x}} \left (1 + \sqrt {3} i\right )}{2 e}\right ) - 1\right ] \]