60.1.304 problem 310
Internal
problem
ID
[10318]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
linear
first
order
Problem
number
:
310
Date
solved
:
Sunday, March 30, 2025 at 04:01:32 PM
CAS
classification
:
[[_homogeneous, `class A`], _exact, _rational, _dAlembert]
\begin{align*} \left (2 y^{3}+5 x^{2} y\right ) y^{\prime }+5 x y^{2}+x^{3}&=0 \end{align*}
✓ Maple. Time used: 0.122 (sec). Leaf size: 125
ode:=(2*y(x)^3+5*x^2*y(x))*diff(y(x),x)+5*x*y(x)^2+x^3 = 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: 23.966 (sec). Leaf size: 295
ode=x^3 + 5*x*y[x]^2 + (5*x^2*y[x] + 2*y[x]^3)*D[y[x],x]==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: 4.711 (sec). Leaf size: 116
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(x**3 + 5*x*y(x)**2 + (5*x**2*y(x) + 2*y(x)**3)*Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = - \frac {\sqrt {2} \sqrt {- 5 x^{2} - \sqrt {C_{1} + 23 x^{4}}}}{2}, \ y{\left (x \right )} = \frac {\sqrt {2} \sqrt {- 5 x^{2} - \sqrt {C_{1} + 23 x^{4}}}}{2}, \ y{\left (x \right )} = - \frac {\sqrt {2} \sqrt {- 5 x^{2} + \sqrt {C_{1} + 23 x^{4}}}}{2}, \ y{\left (x \right )} = \frac {\sqrt {2} \sqrt {- 5 x^{2} + \sqrt {C_{1} + 23 x^{4}}}}{2}\right ]
\]