54.2.192 problem 769
Internal
problem
ID
[12066]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
Additional
non-linear
first
order
Problem
number
:
769
Date
solved
:
Sunday, October 12, 2025 at 02:15:21 AM
CAS
classification
:
[_rational]
\begin{align*} y^{\prime }&=-\frac {i \left (16 i x^{2}+16 y^{4}+8 x^{4} y^{2}+x^{8}\right ) x}{32 y} \end{align*}
✓ Maple. Time used: 0.098 (sec). Leaf size: 193
ode:=diff(y(x),x) = -1/32*I*(16*I*x^2+16*y(x)^4+8*x^4*y(x)^2+x^8)*x/y(x);
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= -\frac {\sqrt {-4 x^{3} \left (\left (1+i\right ) c_1 \operatorname {BesselJ}\left (-\frac {2}{3}, \left (\frac {1}{3}-\frac {i}{3}\right ) x^{3}\right )+\frac {\operatorname {BesselJ}\left (\frac {1}{3}, \left (\frac {1}{3}-\frac {i}{3}\right ) x^{3}\right ) c_1 \,x^{3}}{4}+\left (1+i\right ) \operatorname {BesselY}\left (-\frac {2}{3}, \left (\frac {1}{3}-\frac {i}{3}\right ) x^{3}\right )+\frac {\operatorname {BesselY}\left (\frac {1}{3}, \left (\frac {1}{3}-\frac {i}{3}\right ) x^{3}\right ) x^{3}}{4}\right ) \left (\operatorname {BesselJ}\left (\frac {1}{3}, \left (\frac {1}{3}-\frac {i}{3}\right ) x^{3}\right ) c_1 +\operatorname {BesselY}\left (\frac {1}{3}, \left (\frac {1}{3}-\frac {i}{3}\right ) x^{3}\right )\right )}}{2 \left (\operatorname {BesselJ}\left (\frac {1}{3}, \left (\frac {1}{3}-\frac {i}{3}\right ) x^{3}\right ) c_1 +\operatorname {BesselY}\left (\frac {1}{3}, \left (\frac {1}{3}-\frac {i}{3}\right ) x^{3}\right )\right ) x} \\
y &= \frac {\sqrt {-4 x^{3} \left (\left (1+i\right ) c_1 \operatorname {BesselJ}\left (-\frac {2}{3}, \left (\frac {1}{3}-\frac {i}{3}\right ) x^{3}\right )+\frac {\operatorname {BesselJ}\left (\frac {1}{3}, \left (\frac {1}{3}-\frac {i}{3}\right ) x^{3}\right ) c_1 \,x^{3}}{4}+\left (1+i\right ) \operatorname {BesselY}\left (-\frac {2}{3}, \left (\frac {1}{3}-\frac {i}{3}\right ) x^{3}\right )+\frac {\operatorname {BesselY}\left (\frac {1}{3}, \left (\frac {1}{3}-\frac {i}{3}\right ) x^{3}\right ) x^{3}}{4}\right ) \left (\operatorname {BesselJ}\left (\frac {1}{3}, \left (\frac {1}{3}-\frac {i}{3}\right ) x^{3}\right ) c_1 +\operatorname {BesselY}\left (\frac {1}{3}, \left (\frac {1}{3}-\frac {i}{3}\right ) x^{3}\right )\right )}}{2 \left (\operatorname {BesselJ}\left (\frac {1}{3}, \left (\frac {1}{3}-\frac {i}{3}\right ) x^{3}\right ) c_1 +\operatorname {BesselY}\left (\frac {1}{3}, \left (\frac {1}{3}-\frac {i}{3}\right ) x^{3}\right )\right ) x} \\
\end{align*}
✓ Mathematica. Time used: 36.137 (sec). Leaf size: 836
ode=D[y[x],x] == ((-1/32*I)*x*((16*I)*x^2 + x^8 + 8*x^4*y[x]^2 + 16*y[x]^4))/y[x];
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} \text {Solution too large to show}\end{align*}
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(x*(x**8 + 8*x**4*y(x)**2 + x**2*complex(0, 16) + 16*y(x)**4)*complex(0, 1/32)/y(x) + Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out