60.2.131 problem 707
Internal
problem
ID
[10705]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
Additional
non-linear
first
order
Problem
number
:
707
Date
solved
:
Sunday, March 30, 2025 at 06:23:16 PM
CAS
classification
:
[`y=_G(x,y')`]
\begin{align*} y^{\prime }&=\frac {\left (-\ln \left (-1+y\right )+\ln \left (y+1\right )+2 \ln \left (x \right )\right )^{2} x \left (y+1\right )^{2}}{16} \end{align*}
✓ Maple. Time used: 0.241 (sec). Leaf size: 237
ode:=diff(y(x),x) = 1/16*(-ln(-1+y(x))+ln(1+y(x))+2*ln(x))^2*x*(1+y(x))^2;
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= {\mathrm e}^{\operatorname {RootOf}\left (4 \ln \left (x \right )^{2} x^{2} {\mathrm e}^{\textit {\_Z}}+4 \ln \left ({\mathrm e}^{\textit {\_Z}}+2\right ) \ln \left (x \right ) x^{2} {\mathrm e}^{\textit {\_Z}}+\ln \left ({\mathrm e}^{\textit {\_Z}}+2\right )^{2} x^{2} {\mathrm e}^{\textit {\_Z}}-2 \ln \left (x^{2} \left ({\mathrm e}^{\textit {\_Z}}+2\right )\right ) {\mathrm e}^{\textit {\_Z}} \textit {\_Z} \,x^{2}+{\mathrm e}^{\textit {\_Z}} \textit {\_Z}^{2} x^{2}+8 \ln \left (x \right )^{2} x^{2}+8 \ln \left ({\mathrm e}^{\textit {\_Z}}+2\right ) \ln \left (x \right ) x^{2}+2 \ln \left ({\mathrm e}^{\textit {\_Z}}+2\right )^{2} x^{2}-4 \ln \left (x^{2} \left ({\mathrm e}^{\textit {\_Z}}+2\right )\right ) \textit {\_Z} \,x^{2}+2 \textit {\_Z}^{2} x^{2}-16 \,{\mathrm e}^{\textit {\_Z}}\right )}+1 \\
\int _{\textit {\_b}}^{y}\frac {1}{4 \left (\frac {x^{2} \left (\textit {\_a} +1\right ) \ln \left (-1+\textit {\_a} \right )^{2}}{4}-\left (\textit {\_a} +1\right ) x^{2} \left (\ln \left (x \right )+\frac {\ln \left (\textit {\_a} +1\right )}{2}\right ) \ln \left (-1+\textit {\_a} \right )+\frac {x^{2} \left (\textit {\_a} +1\right ) \ln \left (\textit {\_a} +1\right )^{2}}{4}+\ln \left (x \right ) x^{2} \left (\textit {\_a} +1\right ) \ln \left (\textit {\_a} +1\right )+x^{2} \left (\textit {\_a} +1\right ) \ln \left (x \right )^{2}-4 \textit {\_a} +4\right ) \left (\textit {\_a} +1\right )}d \textit {\_a} -\frac {\ln \left (x \right )}{16}-c_1 &= 0 \\
\end{align*}
✓ Mathematica. Time used: 1.112 (sec). Leaf size: 1391
ode=D[y[x],x] == (x*(2*Log[x] - Log[-1 + y[x]] + Log[1 + y[x]])^2*(1 + y[x])^2)/16;
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*(y(x) + 1)**2*(2*log(x) - log(y(x) - 1) + log(y(x) + 1))**2/16 + Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out