60.2.153 problem 729
Internal
problem
ID
[10727]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
Additional
non-linear
first
order
Problem
number
:
729
Date
solved
:
Sunday, March 30, 2025 at 06:27:38 PM
CAS
classification
:
[_rational]
\begin{align*} y^{\prime }&=\frac {y \left (x -y\right )}{x \left (x -y^{3}\right )} \end{align*}
✓ Maple. Time used: 0.015 (sec). Leaf size: 316
ode:=diff(y(x),x) = y(x)*(x-y(x))/x/(x-y(x)^3);
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= \frac {\left (-27 x +3 \sqrt {24 c_1^{3}-72 c_1^{2} \ln \left (x \right )+72 c_1 \ln \left (x \right )^{2}-24 \ln \left (x \right )^{3}+81 x^{2}}\right )^{{2}/{3}}+6 \ln \left (x \right )-6 c_1}{3 \left (-27 x +3 \sqrt {24 c_1^{3}-72 c_1^{2} \ln \left (x \right )+72 c_1 \ln \left (x \right )^{2}-24 \ln \left (x \right )^{3}+81 x^{2}}\right )^{{1}/{3}}} \\
y &= -\frac {\left (\frac {i \sqrt {3}}{6}+\frac {1}{6}\right ) \left (-27 x +3 \sqrt {24 c_1^{3}-72 c_1^{2} \ln \left (x \right )+72 c_1 \ln \left (x \right )^{2}-24 \ln \left (x \right )^{3}+81 x^{2}}\right )^{{2}/{3}}+\left (-\ln \left (x \right )+c_1 \right ) \left (i \sqrt {3}-1\right )}{\left (-27 x +3 \sqrt {24 c_1^{3}-72 c_1^{2} \ln \left (x \right )+72 c_1 \ln \left (x \right )^{2}-24 \ln \left (x \right )^{3}+81 x^{2}}\right )^{{1}/{3}}} \\
y &= \frac {\frac {\left (i \sqrt {3}-1\right ) \left (-27 x +3 \sqrt {24 c_1^{3}-72 c_1^{2} \ln \left (x \right )+72 c_1 \ln \left (x \right )^{2}-24 \ln \left (x \right )^{3}+81 x^{2}}\right )^{{2}/{3}}}{6}+\left (1+i \sqrt {3}\right ) \left (-\ln \left (x \right )+c_1 \right )}{\left (-27 x +3 \sqrt {24 c_1^{3}-72 c_1^{2} \ln \left (x \right )+72 c_1 \ln \left (x \right )^{2}-24 \ln \left (x \right )^{3}+81 x^{2}}\right )^{{1}/{3}}} \\
\end{align*}
✓ Mathematica. Time used: 6.507 (sec). Leaf size: 320
ode=D[y[x],x] == ((x - y[x])*y[x])/(x*(x - y[x]^3));
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to \frac {2 \sqrt [3]{2} (-\log (x)+c_1)}{\sqrt [3]{54 x+2 \sqrt {729 x^2+(-6 \log (x)+6 c_1){}^3}}}-\frac {\sqrt [3]{54 x+2 \sqrt {729 x^2+(-6 \log (x)+6 c_1){}^3}}}{3 \sqrt [3]{2}} \\
y(x)\to \frac {i \sqrt [3]{2} \left (\sqrt {3}+i\right ) (-\log (x)+c_1)}{\sqrt [3]{54 x+2 \sqrt {729 x^2+(-6 \log (x)+6 c_1){}^3}}}+\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{54 x+2 \sqrt {729 x^2+(-6 \log (x)+6 c_1){}^3}}}{6 \sqrt [3]{2}} \\
y(x)\to \frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{54 x+2 \sqrt {729 x^2+(-6 \log (x)+6 c_1){}^3}}}{6 \sqrt [3]{2}}-\frac {i \sqrt [3]{2} \left (\sqrt {3}-i\right ) (-\log (x)+c_1)}{\sqrt [3]{54 x+2 \sqrt {729 x^2+(-6 \log (x)+6 c_1){}^3}}} \\
y(x)\to 0 \\
\end{align*}
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(Derivative(y(x), x) - (x - y(x))*y(x)/(x*(x - y(x)**3)),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out