29.18.11 problem 487

Internal problem ID [5085]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 487
Date solved : Sunday, March 30, 2025 at 06:36:04 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: 3.679 (sec). Leaf size: 109

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

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

✓ Sympy. Time used: 0.998 (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)
 

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