32.10.10 problem Exercise 35.10, page 504

Internal problem ID [6004]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 8. Special second order equations. Lesson 35. Independent variable x absent
Problem number : Exercise 35.10, page 504
Date solved : Sunday, March 30, 2025 at 10:30:52 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}-y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.053 (sec). Leaf size: 34

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

\begin{align*} y &= 0 \\ y &= -c_1 \left (\operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {-c_1 -c_2 -x}{c_1}}}{c_1}\right )+1\right ) \\ \end{align*}

✓ Mathematica. Time used: 60.103 (sec). Leaf size: 32

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

\[ y(x)\to -c_1 \left (1+W\left (-\frac {e^{-\frac {x+c_1+c_2}{c_1}}}{c_1}\right )\right ) \]

✗ Sympy

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

NotImplementedError : The given ODE -sqrt(-4*y(x)*Derivative(y(x), (x, 2)) + 1)/2 + Derivative(y(x), x) - 1/2 cannot be solved by the factorable group method