60.7.93 problem 1704 (book 6.113)

Internal problem ID [11643]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1704 (book 6.113)
Date solved : Sunday, March 30, 2025 at 08:32:29 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

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

✓ Maple. Time used: 0.022 (sec). Leaf size: 18

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

\[ y = {\mathrm e}^{-\frac {c_1 \,{\mathrm e}^{x}}{2}+\frac {c_2 \,{\mathrm e}^{-x}}{2}} \]

✓ Mathematica. Time used: 1.007 (sec). Leaf size: 63

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

\begin{align*} y(x)\to e^{\frac {1}{2} \left (e^{x+c_2}-c_1 e^{-x-c_2}\right )} \\ y(x)\to e^{\frac {1}{2} \left (e^{-x-c_2}-c_1 e^{x+c_2}\right )} \\ \end{align*}

✗ Sympy

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

TypeError : cannot determine truth value of Relational