60.2.146 problem 722
Internal
problem
ID
[10720]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
Additional
non-linear
first
order
Problem
number
:
722
Date
solved
:
Wednesday, March 05, 2025 at 12:28:34 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+2 y \ln \left (x \right )-y\right ) x} \end{align*}
✓ Maple. Time used: 0.002 (sec). Leaf size: 78
ode:=diff(y(x),x) = -y(x)^3/(-1+2*y(x)*ln(x)-y(x))/x;
dsolve(ode,y(x), singsol=all);
\[
y = \frac {{\mathrm e}^{\operatorname {RootOf}\left (-{\mathrm e}^{\textit {\_Z}} \ln \left (\frac {{\mathrm e}^{\textit {\_Z}}+2}{x^{4}}\right )+{\mathrm e}^{\textit {\_Z}} \ln \left (2\right )+3 c_{1} {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+2\right )}}{1+\left (2 \ln \left (x \right )-1\right ) {\mathrm e}^{\operatorname {RootOf}\left (-{\mathrm e}^{\textit {\_Z}} \ln \left (\frac {{\mathrm e}^{\textit {\_Z}}+2}{x^{4}}\right )+{\mathrm e}^{\textit {\_Z}} \ln \left (2\right )+3 c_{1} {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+2\right )}}
\]
✓ Mathematica. Time used: 0.44 (sec). Leaf size: 122
ode=D[y[x],x] == -(y[x]^3/(x*(-1 - y[x] + 2*Log[x]*y[x])));
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
\text {Solve}\left [\int _1^{-\frac {(1-2 \log (x))^2 \left (-\frac {1}{(2 \log (x)-1)^3}\right )^{2/3} ((5-4 \log (x)) y(x)+2)}{2 \sqrt [3]{2} ((2 \log (x)-1) y(x)-1)}}\frac {2}{2 K[1]^3+3 \sqrt [3]{-2} K[1]+2}dK[1]=\frac {4}{9} 2^{2/3} \log (x) \left (-\frac {1}{(2 \log (x)-1)^3}\right )^{2/3} (1-2 \log (x))^2+c_1,y(x)\right ]
\]
✓ Sympy. Time used: 1.744 (sec). Leaf size: 31
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(Derivative(y(x), x) + y(x)**3/(x*(2*y(x)*log(x) - y(x) - 1)),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
C_{1} - \frac {\left (3 y{\left (x \right )} + 2\right ) e^{- \frac {2}{y{\left (x \right )}}}}{4 y{\left (x \right )}} + e^{- \frac {2}{y{\left (x \right )}}} \log {\left (x \right )} = 0
\]