60.2.231 problem 807

Internal problem ID [10805]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 807
Date solved : Friday, March 14, 2025 at 02:34:00 AM
CAS classification : [NONE]

\begin{align*} y^{\prime }&=-\frac {1}{-x -\textit {\_F1} \left (y-\ln \left (x \right )\right ) y \,{\mathrm e}^{y}} \end{align*}

✓ Maple. Time used: 0.066 (sec). Leaf size: 43

ode:=diff(y(x),x) = -1/(-x-_F1(y(x)-ln(x))*y(x)*exp(y(x))); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.234 (sec). Leaf size: 57

ode=D[y[x],x] == -(-x - E^y[x]*F1[-Log[x] + y[x]]*y[x])^(-1); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [-\int _1^{y(x)-\log (x)}\frac {\text {F1}(K[1]) K[1]+e^{-K[1]}}{\text {F1}(K[1])}dK[1]-y(x) \log (x)+\frac {\log ^2(x)}{2}=-c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
F1 = Function("F1") 
ode = Eq(Derivative(y(x), x) + 1/(-x - F1(y(x) - log(x))*y(x)*exp(y(x))),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out