60.2.148 problem 724

Internal problem ID [10722]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 724
Date solved : Wednesday, March 05, 2025 at 12:28:39 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class C`]]

\begin{align*} y^{\prime }&=-\frac {y^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x} \end{align*}

✓ Maple. Time used: 0.026 (sec). Leaf size: 18

ode:=diff(y(x),x) = -y(x)^3/(-1+y(x)*ln(x)-y(x))/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{-\operatorname {LambertW}\left (c_{1} {\mathrm e}^{-2} x \right )+\ln \left (x \right )-2} \]

✓ Mathematica. Time used: 0.327 (sec). Leaf size: 108

ode=D[y[x],x] == -(y[x]^3/(x*(-1 - y[x] + Log[x]*y[x]))); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{\frac {1-(\log (x)-4) y(x)}{\sqrt [3]{2} \sqrt [3]{-\frac {1}{(\log (x)-1)^3}} (\log (x)-1) ((\log (x)-1) y(x)-1)}}\frac {2}{2 K[1]^3+3 \sqrt [3]{-2} K[1]+2}dK[1]=\frac {1}{9} 2^{2/3} \left (-\frac {1}{(\log (x)-1)^3}\right )^{2/3} \log (x) (\log (x)-1)^2+c_1,y(x)\right ] \]

✓ Sympy. Time used: 1.617 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) + y(x)**3/(x*(y(x)*log(x) - y(x) - 1)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ C_{1} - \frac {\left (2 y{\left (x \right )} + 1\right ) e^{- \frac {1}{y{\left (x \right )}}}}{y{\left (x \right )}} + e^{- \frac {1}{y{\left (x \right )}}} \log {\left (x \right )} = 0 \]