29.24.24 problem 686
Internal
problem
ID
[5277]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
24
Problem
number
:
686
Date
solved
:
Sunday, March 30, 2025 at 07:42:47 AM
CAS
classification
:
[[_homogeneous, `class A`], _exact, _rational, _dAlembert]
\begin{align*} \left (5 x^{2}+2 y^{2}\right ) y y^{\prime }+x \left (x^{2}+5 y^{2}\right )&=0 \end{align*}
✓ Maple. Time used: 0.033 (sec). Leaf size: 125
ode:=(5*x^2+2*y(x)^2)*y(x)*diff(y(x),x)+x*(x^2+5*y(x)^2) = 0;
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= -\frac {\sqrt {-10 c_1 \,x^{2}-2 \sqrt {23 x^{4} c_1^{2}+2}}}{2 \sqrt {c_1}} \\
y &= \frac {\sqrt {-10 c_1 \,x^{2}-2 \sqrt {23 x^{4} c_1^{2}+2}}}{2 \sqrt {c_1}} \\
y &= -\frac {\sqrt {-10 c_1 \,x^{2}+2 \sqrt {23 x^{4} c_1^{2}+2}}}{2 \sqrt {c_1}} \\
y &= \frac {\sqrt {-10 c_1 \,x^{2}+2 \sqrt {23 x^{4} c_1^{2}+2}}}{2 \sqrt {c_1}} \\
\end{align*}
✓ Mathematica. Time used: 23.791 (sec). Leaf size: 295
ode=(5*x^2+2*y[x]^2)*y[x]*D[y[x],x]+x*(x^2+5*y[x]^2)==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to -\frac {\sqrt {-5 x^2-\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}} \\
y(x)\to \frac {\sqrt {-5 x^2-\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}} \\
y(x)\to -\frac {\sqrt {-5 x^2+\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}} \\
y(x)\to \frac {\sqrt {-5 x^2+\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}} \\
y(x)\to -\frac {\sqrt {-\sqrt {23} \sqrt {x^4}-5 x^2}}{\sqrt {2}} \\
y(x)\to \frac {\sqrt {-\sqrt {23} \sqrt {x^4}-5 x^2}}{\sqrt {2}} \\
y(x)\to -\frac {\sqrt {\sqrt {23} \sqrt {x^4}-5 x^2}}{\sqrt {2}} \\
y(x)\to \frac {\sqrt {\sqrt {23} \sqrt {x^4}-5 x^2}}{\sqrt {2}} \\
\end{align*}
✓ Sympy. Time used: 4.913 (sec). Leaf size: 116
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(x*(x**2 + 5*y(x)**2) + (5*x**2 + 2*y(x)**2)*y(x)*Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = - \frac {\sqrt {2} \sqrt {- 5 x^{2} - \sqrt {C_{1} + 23 x^{4}}}}{2}, \ y{\left (x \right )} = \frac {\sqrt {2} \sqrt {- 5 x^{2} - \sqrt {C_{1} + 23 x^{4}}}}{2}, \ y{\left (x \right )} = - \frac {\sqrt {2} \sqrt {- 5 x^{2} + \sqrt {C_{1} + 23 x^{4}}}}{2}, \ y{\left (x \right )} = \frac {\sqrt {2} \sqrt {- 5 x^{2} + \sqrt {C_{1} + 23 x^{4}}}}{2}\right ]
\]