23.1.500 problem 490

Internal problem ID [5107]
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 : 490
Date solved : Tuesday, September 30, 2025 at 11:37:32 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class C`], _dAlembert]

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

✓ Maple. Time used: 0.083 (sec). Leaf size: 28

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

\[ y = \frac {-x \operatorname {LambertW}\left (-c_1 \left (-2+x \right )\right )+x -2}{2 \operatorname {LambertW}\left (-c_1 \left (-2+x \right )\right )} \]

✓ Mathematica. Time used: 0.052 (sec). Leaf size: 66

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

\[ \text {Solve}\left [\int _1^{-\frac {x+4 y(x)+2}{2 \sqrt [3]{2} (x+y(x)-1)}}\frac {1}{K[1]^3-\frac {3 K[1]}{2^{2/3}}+1}dK[1]=\frac {1}{9} 2^{2/3} \log (x-2)+c_1,y(x)\right ] \]

✓ Sympy. Time used: 0.665 (sec). Leaf size: 19

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

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