60.2.62 problem 638

Internal problem ID [10636]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 638
Date solved : Sunday, March 30, 2025 at 06:13:25 PM
CAS classification : [`x=_G(y,y')`]

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

✓ Maple. Time used: 0.034 (sec). Leaf size: 36

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

\[ -\int _{\textit {\_b}}^{y}-\frac {1}{\textit {\_a} \left (x \ln \left (x \right )-\ln \left (\ln \left (\textit {\_a} \right )\right ) x +\ln \left (\textit {\_a} \right )\right )}d \textit {\_a} -c_1 = 0 \]

✓ Mathematica. Time used: 0.091 (sec). Leaf size: 41

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

\[ \text {Solve}\left [\int _1^{y(x)}\frac {1}{K[1] (x \log (x)+\log (K[1])-x \log (\log (K[1])))}dK[1]=-\log (x)+c_1,y(x)\right ] \]

✗ Sympy

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

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