60.2.9 problem 585
Internal
problem
ID
[10583]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
Additional
non-linear
first
order
Problem
number
:
585
Date
solved
:
Sunday, March 30, 2025 at 06:08:30 PM
CAS
classification
:
[[_1st_order, `_with_symmetry_[F(x),G(y)]`]]
\begin{align*} y^{\prime }&=F \left (\ln \left (\ln \left (y\right )\right )-\ln \left (x \right )\right ) y \end{align*}
✓ Maple. Time used: 0.227 (sec). Leaf size: 138
ode:=diff(y(x),x) = F(ln(ln(y(x)))-ln(x))*y(x);
dsolve(ode,y(x), singsol=all);
\[
-\int _{\textit {\_b}}^{x}\frac {F \left (\ln \left (\ln \left (y\right )\right )-\ln \left (\textit {\_a} \right )\right )}{\textit {\_a} F \left (\ln \left (\ln \left (y\right )\right )-\ln \left (\textit {\_a} \right )\right )-\ln \left (y\right )}d \textit {\_a} -\int _{}^{y}\frac {-1+\int _{\textit {\_b}}^{x}\frac {D\left (F \right )\left (\ln \left (\ln \left (\textit {\_f} \right )\right )-\ln \left (\textit {\_a} \right )\right )-F \left (\ln \left (\ln \left (\textit {\_f} \right )\right )-\ln \left (\textit {\_a} \right )\right )}{\left (\textit {\_a} F \left (\ln \left (\ln \left (\textit {\_f} \right )\right )-\ln \left (\textit {\_a} \right )\right )-\ln \left (\textit {\_f} \right )\right )^{2}}d \textit {\_a} \left (x F \left (\ln \left (\ln \left (\textit {\_f} \right )\right )-\ln \left (x \right )\right )-\ln \left (\textit {\_f} \right )\right )}{\textit {\_f} \left (x F \left (\ln \left (\ln \left (\textit {\_f} \right )\right )-\ln \left (x \right )\right )-\ln \left (\textit {\_f} \right )\right )}d \textit {\_f} +c_1 = 0
\]
✓ Mathematica. Time used: 0.144 (sec). Leaf size: 205
ode=D[y[x],x] == F[-Log[x] + Log[Log[y[x]]]]*y[x];
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
\text {Solve}\left [\int _1^{y(x)}\left (\frac {1}{K[2] (x F(\log (\log (K[2]))-\log (x))-\log (K[2]))}-\int _1^x\left (\frac {F(\log (\log (K[2]))-\log (K[1])) \left (\frac {K[1] F''(\log (\log (K[2]))-\log (K[1]))}{K[2] \log (K[2])}-\frac {1}{K[2]}\right )}{(F(\log (\log (K[2]))-\log (K[1])) K[1]-\log (K[2]))^2}-\frac {F''(\log (\log (K[2]))-\log (K[1]))}{K[2] (F(\log (\log (K[2]))-\log (K[1])) K[1]-\log (K[2])) \log (K[2])}\right )dK[1]\right )dK[2]+\int _1^x-\frac {F(\log (\log (y(x)))-\log (K[1]))}{F(\log (\log (y(x)))-\log (K[1])) K[1]-\log (y(x))}dK[1]=c_1,y(x)\right ]
\]
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
F = Function("F")
ode = Eq(-F(-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 -F(-log(x) + log(log(y(x))))*y(x) + Derivative(y(x), x) cannot be solved by the lie group method