54.2.64 problem 640

Internal problem ID [11938]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 640
Date solved : Sunday, October 12, 2025 at 02:04:32 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }&=\frac {y}{\ln \left (\ln \left (y\right )\right )-\ln \left (x \right )+1} \end{align*}

✓ Maple. Time used: 0.029 (sec). Leaf size: 45

ode:=diff(y(x),x) = 1/(ln(ln(y(x)))-ln(x)+1)*y(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.125 (sec). Leaf size: 53

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

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

✗ Sympy

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

IndexError : Index out of range: a[1]