54.2.268 problem 846
Internal
problem
ID
[12142]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
Additional
non-linear
first
order
Problem
number
:
846
Date
solved
:
Sunday, October 12, 2025 at 02:22:30 AM
CAS
classification
:
[`y=_G(x,y')`]
\begin{align*} y^{\prime }&=\frac {1}{-x +\left (\frac {1}{y}+1\right ) x +\textit {\_F1} \left (\left (\frac {1}{y}+1\right ) x \right ) x^{2}-\textit {\_F1} \left (\left (\frac {1}{y}+1\right ) x \right ) x^{2} \left (\frac {1}{y}+1\right )} \end{align*}
✓ Maple. Time used: 0.041 (sec). Leaf size: 72
ode:=diff(y(x),x) = 1/(-x+(1/y(x)+1)*x+_F1((1/y(x)+1)*x)*x^2-_F1((1/y(x)+1)*x)*x^2*(1/y(x)+1));
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= \operatorname {RootOf}\left (\textit {\_F1} \left (\frac {\left (1+\textit {\_Z} \right ) x}{\textit {\_Z}}\right ) x \textit {\_Z} +\textit {\_F1} \left (\frac {\left (1+\textit {\_Z} \right ) x}{\textit {\_Z}}\right ) x -\textit {\_Z} \right ) \\
y &= {\mathrm e}^{\operatorname {RootOf}\left (-\textit {\_Z} -\int _{}^{-\frac {x}{-1+{\mathrm e}^{-\textit {\_Z}}}}\frac {1}{\textit {\_a} \left (\textit {\_F1} \left (\textit {\_a} \right ) \textit {\_a} -1\right )}d \textit {\_a} +c_1 \right )}-1 \\
\end{align*}
✓ Mathematica. Time used: 0.4 (sec). Leaf size: 346
ode=D[y[x],x] == (-x + x^2*F1[x*(1 + y[x]^(-1))] + x*(1 + y[x]^(-1)) - x^2*F1[x*(1 + y[x]^(-1))]*(1 + y[x]^(-1)))^(-1);
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
\text {Solve}\left [\int _1^{y(x)}\left (\frac {x \text {F1}\left (x \left (1+\frac {1}{K[2]}\right )\right )-1}{x \text {F1}\left (x \left (1+\frac {1}{K[2]}\right )\right )+x K[2] \text {F1}\left (x \left (1+\frac {1}{K[2]}\right )\right )-K[2]}-\int _1^x\left (\frac {\text {F1}\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )-\frac {K[1] \text {F1}''\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )}{K[2]}-\frac {K[1] \text {F1}''\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )}{K[2]^2}}{K[1] \left (K[2] \text {F1}\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )+\text {F1}\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )\right )-K[2]}-\frac {\left (K[2] \text {F1}\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )+\text {F1}\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )\right ) \left (K[1] \left (\text {F1}\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )-\frac {K[1] \text {F1}''\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )}{K[2]}-\frac {K[1] \text {F1}''\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )}{K[2]^2}\right )-1\right )}{\left (K[1] \left (K[2] \text {F1}\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )+\text {F1}\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )\right )-K[2]\right )^2}\right )dK[1]\right )dK[2]+\int _1^x\left (\frac {y(x) \text {F1}\left (K[1] \left (1+\frac {1}{y(x)}\right )\right )+\text {F1}\left (K[1] \left (1+\frac {1}{y(x)}\right )\right )}{K[1] \left (y(x) \text {F1}\left (K[1] \left (1+\frac {1}{y(x)}\right )\right )+\text {F1}\left (K[1] \left (1+\frac {1}{y(x)}\right )\right )\right )-y(x)}-\frac {1}{K[1]}\right )dK[1]=c_1,y(x)\right ]
\]
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
F1 = Function("F1")
ode = Eq(Derivative(y(x), x) - 1/(-x**2*(1 + 1/y(x))*F1(x*(1 + 1/y(x))) + x**2*F1(x*(1 + 1/y(x))) + x*(1 + 1/y(x)) - x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out