29.19.23 problem 536
Internal
problem
ID
[5132]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
19
Problem
number
:
536
Date
solved
:
Tuesday, March 04, 2025 at 08:10:56 PM
CAS
classification
:
[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
\begin{align*} x \left (2 x^{3}+y\right ) y^{\prime }&=6 y^{2} \end{align*}
✓ Maple. Time used: 0.891 (sec). Leaf size: 193
ode:=x*(2*x^3+y(x))*diff(y(x),x) = 6*y(x)^2;
dsolve(ode,y(x), singsol=all);
\begin{align*}
y \left (x \right ) &= -\frac {x^{3} \left (-x^{3}+\sqrt {x^{3} \left (x^{3}+8 c_{1} \right )}-4 c_{1} \right )}{2 c_{1}} \\
y \left (x \right ) &= \frac {x^{3} \left (x^{3}+\sqrt {x^{3} \left (x^{3}+8 c_{1} \right )}+4 c_{1} \right )}{2 c_{1}} \\
y \left (x \right ) &= -\frac {x^{3} \left (-x^{3}+\sqrt {x^{3} \left (x^{3}+8 c_{1} \right )}-4 c_{1} \right )}{2 c_{1}} \\
y \left (x \right ) &= \frac {x^{3} \left (x^{3}+\sqrt {x^{3} \left (x^{3}+8 c_{1} \right )}+4 c_{1} \right )}{2 c_{1}} \\
y \left (x \right ) &= -\frac {x^{3} \left (-x^{3}+\sqrt {x^{3} \left (x^{3}+8 c_{1} \right )}-4 c_{1} \right )}{2 c_{1}} \\
y \left (x \right ) &= \frac {x^{3} \left (x^{3}+\sqrt {x^{3} \left (x^{3}+8 c_{1} \right )}+4 c_{1} \right )}{2 c_{1}} \\
\end{align*}
✓ Mathematica. Time used: 1.285 (sec). Leaf size: 123
ode=x(2 x^3+y[x])D[y[x],x]==6 y[x]^2;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to 2 x^3 \left (-1+\frac {2}{1-\frac {4 x^{3/2}}{\sqrt {16 x^3+c_1}}}\right ) \\
y(x)\to 2 x^3 \left (-1+\frac {2}{1+\frac {4 x^{3/2}}{\sqrt {16 x^3+c_1}}}\right ) \\
y(x)\to 0 \\
y(x)\to 2 x^3 \\
y(x)\to \frac {2 \left (\left (x^3\right )^{3/2}-x^{9/2}\right )}{x^{3/2}+\sqrt {x^3}} \\
\end{align*}
✓ Sympy. Time used: 1.287 (sec). Leaf size: 78
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(x*(2*x**3 + y(x))*Derivative(y(x), x) - 6*y(x)**2,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = - \frac {3 C_{1} \sqrt {x^{9} \left (9 C_{1}^{2} x^{3} + 8\right )}}{2} + \frac {x^{3} \left (9 C_{1}^{2} x^{3} + 4\right )}{2}, \ y{\left (x \right )} = \frac {3 C_{1} \sqrt {x^{9} \left (9 C_{1}^{2} x^{3} + 8\right )}}{2} + \frac {x^{3} \left (9 C_{1}^{2} x^{3} + 4\right )}{2}\right ]
\]