29.23.25 problem 656
Internal
problem
ID
[5247]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
23
Problem
number
:
656
Date
solved
:
Sunday, March 30, 2025 at 07:30:56 AM
CAS
classification
:
[_rational]
\begin{align*} 3 x \left (x +y^{2}\right ) y^{\prime }+x^{3}-3 x y-2 y^{3}&=0 \end{align*}
✓ Maple. Time used: 0.005 (sec). Leaf size: 356
ode:=3*x*(x+y(x)^2)*diff(y(x),x)+x^3-3*x*y(x)-2*y(x)^3 = 0;
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= \frac {\left (-4 c_1 \,x^{2}-4 x^{3}+4 \sqrt {x^{3} \left (x \,c_1^{2}+2 c_1 \,x^{2}+x^{3}+4\right )}\right )^{{2}/{3}}-4 x}{2 \left (-4 c_1 \,x^{2}-4 x^{3}+4 \sqrt {x^{3} \left (x \,c_1^{2}+2 c_1 \,x^{2}+x^{3}+4\right )}\right )^{{1}/{3}}} \\
y &= -\frac {i \sqrt {3}\, \left (-4 c_1 \,x^{2}-4 x^{3}+4 \sqrt {x^{3} \left (x \,c_1^{2}+2 c_1 \,x^{2}+x^{3}+4\right )}\right )^{{2}/{3}}+4 i \sqrt {3}\, x +\left (-4 c_1 \,x^{2}-4 x^{3}+4 \sqrt {x^{3} \left (x \,c_1^{2}+2 c_1 \,x^{2}+x^{3}+4\right )}\right )^{{2}/{3}}-4 x}{4 \left (-4 c_1 \,x^{2}-4 x^{3}+4 \sqrt {x^{3} \left (x \,c_1^{2}+2 c_1 \,x^{2}+x^{3}+4\right )}\right )^{{1}/{3}}} \\
y &= \frac {i \sqrt {3}\, \left (-4 c_1 \,x^{2}-4 x^{3}+4 \sqrt {x^{3} \left (x \,c_1^{2}+2 c_1 \,x^{2}+x^{3}+4\right )}\right )^{{2}/{3}}+4 i \sqrt {3}\, x -\left (-4 c_1 \,x^{2}-4 x^{3}+4 \sqrt {x^{3} \left (x \,c_1^{2}+2 c_1 \,x^{2}+x^{3}+4\right )}\right )^{{2}/{3}}+4 x}{4 \left (-4 c_1 \,x^{2}-4 x^{3}+4 \sqrt {x^{3} \left (x \,c_1^{2}+2 c_1 \,x^{2}+x^{3}+4\right )}\right )^{{1}/{3}}} \\
\end{align*}
✓ Mathematica. Time used: 49.846 (sec). Leaf size: 362
ode=3 x(x+y[x]^2)D[y[x],x]+x^3-3 x y[x]-2 y[x]^3==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to \frac {\sqrt [3]{-x^3+c_1 x^2+\sqrt {x^3 \left (x^3-2 c_1 x^2+c_1{}^2 x+4\right )}}}{\sqrt [3]{2}}-\frac {\sqrt [3]{2} x}{\sqrt [3]{-x^3+c_1 x^2+\sqrt {x^3 \left (x^3-2 c_1 x^2+c_1{}^2 x+4\right )}}} \\
y(x)\to \frac {i 2^{2/3} \left (\sqrt {3}+i\right ) \left (-x^3+c_1 x^2+\sqrt {x^3 \left (x^3-2 c_1 x^2+c_1{}^2 x+4\right )}\right ){}^{2/3}+\sqrt [3]{2} \left (2+2 i \sqrt {3}\right ) x}{4 \sqrt [3]{-x^3+c_1 x^2+\sqrt {x^3 \left (x^3-2 c_1 x^2+c_1{}^2 x+4\right )}}} \\
y(x)\to \frac {\sqrt [3]{2} \left (2-2 i \sqrt {3}\right ) x-i 2^{2/3} \left (\sqrt {3}-i\right ) \left (-x^3+c_1 x^2+\sqrt {x^3 \left (x^3-2 c_1 x^2+c_1{}^2 x+4\right )}\right ){}^{2/3}}{4 \sqrt [3]{-x^3+c_1 x^2+\sqrt {x^3 \left (x^3-2 c_1 x^2+c_1{}^2 x+4\right )}}} \\
\end{align*}
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(x**3 + 3*x*(x + y(x)**2)*Derivative(y(x), x) - 3*x*y(x) - 2*y(x)**3,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out