60.2.63 problem 639

Internal problem ID [10637]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 639
Date solved : Sunday, March 30, 2025 at 06:13:30 PM
CAS classification : [`y=_G(x,y')`]

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

✓ Maple. Time used: 0.035 (sec). Leaf size: 48

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

\[ -\int _{\textit {\_b}}^{y}\frac {1}{\textit {\_a} \left (\ln \left (\ln \left (\textit {\_a} \right )\right )^{2} x -2 \ln \left (\ln \left (\textit {\_a} \right )\right ) \ln \left (x \right ) x +\ln \left (x \right )^{2} x -\ln \left (\textit {\_a} \right )\right )}d \textit {\_a} -c_1 = 0 \]

✓ Mathematica. Time used: 0.121 (sec). Leaf size: 53

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

\[ \text {Solve}\left [\int _1^{y(x)}\frac {1}{K[1] \left (x \log ^2(x)-2 x \log (\log (K[1])) \log (x)+x \log ^2(\log (K[1]))-\log (K[1])\right )}dK[1]=\log (x)+c_1,y(x)\right ] \]

✗ Sympy

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

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