32.10.1 problem Exercise 35.1, page 504

Internal problem ID [5995]
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 35.1, page 504
Date solved : Sunday, March 30, 2025 at 10:29:20 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

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

✓ Maple. Time used: 0.049 (sec). Leaf size: 16

ode:=diff(diff(y(x),x),x) = 2*y(x)*diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\tan \left (\frac {c_2 +x}{c_1}\right )}{c_1} \]

✓ Mathematica. Time used: 12.497 (sec). Leaf size: 24

ode=D[y[x],{x,2}]==2*y[x]*D[y[x],x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \sqrt {c_1} \tan \left (\sqrt {c_1} (x+c_2)\right ) \]

✗ Sympy

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

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