29.18.19 problem 495

Internal problem ID [5093]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 495
Date solved : Sunday, March 30, 2025 at 06:37:16 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (1+x +9 y\right ) y^{\prime }+1+x +5 y&=0 \end{align*}

✓ Maple. Time used: 0.077 (sec). Leaf size: 29

ode:=(1+x+9*y(x))*diff(y(x),x)+1+x+5*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\left (x +1\right ) \left (2+3 \operatorname {LambertW}\left (\frac {2 c_1 \left (x +1\right )}{3}\right )\right )}{9 \operatorname {LambertW}\left (\frac {2 c_1 \left (x +1\right )}{3}\right )} \]

✓ Mathematica. Time used: 41.833 (sec). Leaf size: 145

ode=(1+x+9 y[x])D[y[x],x]+1+x+5 y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {(-2)^{2/3} \left ((x+1) \left (3 \log \left (-\frac {6 (-2)^{2/3} (x+1)}{9 y(x)+x+1}\right )-3 \log \left (\frac {9 (-2)^{2/3} (3 y(x)+x+1)}{9 y(x)+x+1}\right )+1\right )+9 y(x) \left (\log \left (-\frac {6 (-2)^{2/3} (x+1)}{9 y(x)+x+1}\right )-\log \left (\frac {9 (-2)^{2/3} (3 y(x)+x+1)}{9 y(x)+x+1}\right )+1\right )\right )}{27 (3 y(x)+x+1)}=\frac {1}{9} (-2)^{2/3} \log (x+1)+c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x + (x + 9*y(x) + 1)*Derivative(y(x), x) + 5*y(x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

RecursionError : maximum recursion depth exceeded