29.25.17 problem 714
Internal
problem
ID
[5304]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
25
Problem
number
:
714
Date
solved
:
Sunday, March 30, 2025 at 07:52:45 AM
CAS
classification
:
[[_homogeneous, `class G`], _rational]
\begin{align*} x \left (1-x^{2} y^{4}\right ) y^{\prime }+y&=0 \end{align*}
✓ Maple. Time used: 0.047 (sec). Leaf size: 133
ode:=x*(1-y(x)^4*x^2)*diff(y(x),x)+y(x) = 0;
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= -\frac {\sqrt {2}\, \sqrt {\left (x -\sqrt {-4 c_1^{2}+x^{2}}\right ) c_1 x}}{2 c_1 x} \\
y &= \frac {\sqrt {2}\, \sqrt {\left (x -\sqrt {-4 c_1^{2}+x^{2}}\right ) c_1 x}}{2 c_1 x} \\
y &= -\frac {\sqrt {2}\, \sqrt {c_1 x \left (x +\sqrt {-4 c_1^{2}+x^{2}}\right )}}{2 c_1 x} \\
y &= \frac {\sqrt {2}\, \sqrt {c_1 x \left (x +\sqrt {-4 c_1^{2}+x^{2}}\right )}}{2 c_1 x} \\
\end{align*}
✓ Mathematica. Time used: 12.028 (sec). Leaf size: 172
ode=x(1-x^2 y[x]^4)D[y[x],x]+y[x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to -\sqrt {c_1-\frac {\sqrt {x^2 \left (-1+c_1{}^2 x^2\right )}}{x^2}} \\
y(x)\to \sqrt {c_1-\frac {\sqrt {x^2 \left (-1+c_1{}^2 x^2\right )}}{x^2}} \\
y(x)\to -\sqrt {\frac {\sqrt {x^2 \left (-1+c_1{}^2 x^2\right )}}{x^2}+c_1} \\
y(x)\to \sqrt {\frac {\sqrt {x^2 \left (-1+c_1{}^2 x^2\right )}}{x^2}+c_1} \\
y(x)\to 0 \\
y(x)\to -\frac {1}{\sqrt [4]{-x^2}} \\
y(x)\to \frac {1}{\sqrt [4]{-x^2}} \\
\end{align*}
✓ Sympy. Time used: 7.956 (sec). Leaf size: 126
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(x*(-x**2*y(x)**4 + 1)*Derivative(y(x), x) + y(x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = - \frac {\sqrt {2} \sqrt {e^{C_{1}} - \frac {\sqrt {x^{2} e^{2 C_{1}} - 4}}{x}}}{2}, \ y{\left (x \right )} = \frac {\sqrt {2} \sqrt {e^{C_{1}} - \frac {\sqrt {x^{2} e^{2 C_{1}} - 4}}{x}}}{2}, \ y{\left (x \right )} = - \frac {\sqrt {2} \sqrt {e^{C_{1}} + \frac {\sqrt {x^{2} e^{2 C_{1}} - 4}}{x}}}{2}, \ y{\left (x \right )} = \frac {\sqrt {2} \sqrt {e^{C_{1}} + \frac {\sqrt {x^{2} e^{2 C_{1}} - 4}}{x}}}{2}\right ]
\]