29.25.3 problem 700
Internal
problem
ID
[5290]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
25
Problem
number
:
700
Date
solved
:
Tuesday, March 04, 2025 at 09:16:18 PM
CAS
classification
:
[_rational]
\begin{align*} x \left (1-2 x y^{3}\right ) y^{\prime }+\left (1-2 x^{3} y\right ) y&=0 \end{align*}
✓ Maple. Time used: 0.011 (sec). Leaf size: 357
ode:=x*(1-2*x*y(x)^3)*diff(y(x),x)+(1-2*x^3*y(x))*y(x) = 0;
dsolve(ode,y(x), singsol=all);
\begin{align*}
y \left (x \right ) &= -\frac {\left (-{\left (\left (-9+\sqrt {12 x^{8}-36 c_{1} x^{6}+36 c_{1}^{2} x^{4}-12 c_{1}^{3} x^{2}+81}\right ) x^{2}\right )}^{{2}/{3}}+12^{{1}/{3}} x^{2} \left (x^{2}-c_{1} \right )\right ) 12^{{1}/{3}}}{6 {\left (\left (-9+\sqrt {12 x^{8}-36 c_{1} x^{6}+36 c_{1}^{2} x^{4}-12 c_{1}^{3} x^{2}+81}\right ) x^{2}\right )}^{{1}/{3}} x} \\
y \left (x \right ) &= -\frac {2^{{2}/{3}} 3^{{1}/{3}} \left (\left (1+i \sqrt {3}\right ) {\left (\left (-9+\sqrt {12 x^{8}-36 c_{1} x^{6}+36 c_{1}^{2} x^{4}-12 c_{1}^{3} x^{2}+81}\right ) x^{2}\right )}^{{2}/{3}}+2^{{2}/{3}} x^{2} \left (i 3^{{5}/{6}}-3^{{1}/{3}}\right ) \left (x^{2}-c_{1} \right )\right )}{12 {\left (\left (-9+\sqrt {12 x^{8}-36 c_{1} x^{6}+36 c_{1}^{2} x^{4}-12 c_{1}^{3} x^{2}+81}\right ) x^{2}\right )}^{{1}/{3}} x} \\
y \left (x \right ) &= \frac {2^{{2}/{3}} 3^{{1}/{3}} \left (\left (i \sqrt {3}-1\right ) {\left (\left (-9+\sqrt {12 x^{8}-36 c_{1} x^{6}+36 c_{1}^{2} x^{4}-12 c_{1}^{3} x^{2}+81}\right ) x^{2}\right )}^{{2}/{3}}+2^{{2}/{3}} x^{2} \left (i 3^{{5}/{6}}+3^{{1}/{3}}\right ) \left (x^{2}-c_{1} \right )\right )}{12 {\left (\left (-9+\sqrt {12 x^{8}-36 c_{1} x^{6}+36 c_{1}^{2} x^{4}-12 c_{1}^{3} x^{2}+81}\right ) x^{2}\right )}^{{1}/{3}} x} \\
\end{align*}
✓ Mathematica. Time used: 39.252 (sec). Leaf size: 358
ode=x(1-2 x y[x]^3)D[y[x],x]+(1-2 x^3 y[x])y[x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to \frac {\sqrt [3]{2} \left (-x^3+c_1 x\right )}{\sqrt [3]{-27 x^2+\sqrt {729 x^4+108 x^3 \left (x^3-c_1 x\right ){}^3}}}+\frac {\sqrt [3]{-27 x^2+\sqrt {729 x^4+108 x^3 \left (x^3-c_1 x\right ){}^3}}}{3 \sqrt [3]{2} x} \\
y(x)\to \frac {\left (1+i \sqrt {3}\right ) \left (x^3-c_1 x\right )}{2^{2/3} \sqrt [3]{-27 x^2+\sqrt {729 x^4+108 x^3 \left (x^3-c_1 x\right ){}^3}}}-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{-27 x^2+\sqrt {729 x^4+108 x^3 \left (x^3-c_1 x\right ){}^3}}}{6 \sqrt [3]{2} x} \\
y(x)\to \frac {\left (1-i \sqrt {3}\right ) \left (x^3-c_1 x\right )}{2^{2/3} \sqrt [3]{-27 x^2+\sqrt {729 x^4+108 x^3 \left (x^3-c_1 x\right ){}^3}}}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-27 x^2+\sqrt {729 x^4+108 x^3 \left (x^3-c_1 x\right ){}^3}}}{6 \sqrt [3]{2} x} \\
\end{align*}
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(x*(-2*x*y(x)**3 + 1)*Derivative(y(x), x) + (-2*x**3*y(x) + 1)*y(x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out