60.2.167 problem 743
Internal
problem
ID
[10741]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
Additional
non-linear
first
order
Problem
number
:
743
Date
solved
:
Sunday, March 30, 2025 at 06:32:13 PM
CAS
classification
:
[_rational]
\begin{align*} y^{\prime }&=-\frac {i \left (8 i x +16 y^{4}+8 x^{2} y^{2}+x^{4}\right )}{32 y} \end{align*}
✓ Maple. Time used: 0.078 (sec). Leaf size: 276
ode:=diff(y(x),x) = -1/32*I*(8*I*x+16*y(x)^4+8*x^2*y(x)^2+x^4)/y(x);
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= -\frac {\sqrt {2}\, \sqrt {\left (c_1 \left (1+i \sqrt {3}\right ) \operatorname {AiryAi}\left (1, \frac {\left (i-\sqrt {3}\right ) x}{2}\right )+\left (1+i \sqrt {3}\right ) \operatorname {AiryBi}\left (1, \frac {\left (i-\sqrt {3}\right ) x}{2}\right )-\frac {x^{2} \left (\operatorname {AiryAi}\left (\frac {\left (i-\sqrt {3}\right ) x}{2}\right ) c_1 +\operatorname {AiryBi}\left (\frac {\left (i-\sqrt {3}\right ) x}{2}\right )\right )}{2}\right ) \left (\operatorname {AiryAi}\left (\frac {\left (i-\sqrt {3}\right ) x}{2}\right ) c_1 +\operatorname {AiryBi}\left (\frac {\left (i-\sqrt {3}\right ) x}{2}\right )\right )}}{2 \operatorname {AiryAi}\left (\frac {\left (i-\sqrt {3}\right ) x}{2}\right ) c_1 +2 \operatorname {AiryBi}\left (\frac {\left (i-\sqrt {3}\right ) x}{2}\right )} \\
y &= \frac {\sqrt {2}\, \sqrt {\left (c_1 \left (1+i \sqrt {3}\right ) \operatorname {AiryAi}\left (1, \frac {\left (i-\sqrt {3}\right ) x}{2}\right )+\left (1+i \sqrt {3}\right ) \operatorname {AiryBi}\left (1, \frac {\left (i-\sqrt {3}\right ) x}{2}\right )-\frac {x^{2} \left (\operatorname {AiryAi}\left (\frac {\left (i-\sqrt {3}\right ) x}{2}\right ) c_1 +\operatorname {AiryBi}\left (\frac {\left (i-\sqrt {3}\right ) x}{2}\right )\right )}{2}\right ) \left (\operatorname {AiryAi}\left (\frac {\left (i-\sqrt {3}\right ) x}{2}\right ) c_1 +\operatorname {AiryBi}\left (\frac {\left (i-\sqrt {3}\right ) x}{2}\right )\right )}}{2 \operatorname {AiryAi}\left (\frac {\left (i-\sqrt {3}\right ) x}{2}\right ) c_1 +2 \operatorname {AiryBi}\left (\frac {\left (i-\sqrt {3}\right ) x}{2}\right )} \\
\end{align*}
✓ Mathematica. Time used: 5.376 (sec). Leaf size: 553
ode=D[y[x],x] == ((-1/32*I)*((8*I)*x + x^4 + 8*x^2*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**4 + 8*x**2*y(x)**2 + x*complex(0, 8) + 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