89.10.29 problem 30

Internal problem ID [24522]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 77
Problem number : 30
Date solved : Thursday, October 02, 2025 at 10:45:16 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x -6 y+2+2 \left (x +2 y+2\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.054 (sec). Leaf size: 27

ode:=x-6*y(x)+2+2*(x+2*y(x)+2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.606 (sec). Leaf size: 143

ode=( x-6*y[x]+2)+2*( x+2*y[x]+2 )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {2^{2/3} \left ((x+2) \left (\log \left (\frac {6\ 2^{2/3} (x+2)}{2 y(x)+x+2}\right )-\log \left (-\frac {3\ 2^{2/3} (-2 y(x)+x+2)}{2 y(x)+x+2}\right )-1\right )-2 y(x) \left (\log \left (\frac {6\ 2^{2/3} (x+2)}{2 y(x)+x+2}\right )-\log \left (-\frac {3\ 2^{2/3} (-2 y(x)+x+2)}{2 y(x)+x+2}\right )+1\right )\right )}{9 (-2 y(x)+x+2)}=\frac {1}{9} 2^{2/3} \log (x+2)+c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x + (2*x + 4*y(x) + 4)*Derivative(y(x), x) - 6*y(x) + 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

RecursionError : maximum recursion depth exceeded