60.2.166 problem 742
Internal
problem
ID
[10740]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
Additional
non-linear
first
order
Problem
number
:
742
Date
solved
:
Friday, March 14, 2025 at 02:26:21 AM
CAS
classification
:
unknown
\begin{align*} y^{\prime }&=-\frac {\cos \left (y\right ) \left (x -\cos \left (y\right )+1\right )}{\left (x \sin \left (y\right )-1\right ) \left (x +1\right )} \end{align*}
✓ Maple. Time used: 0.743 (sec). Leaf size: 239
ode:=diff(y(x),x) = -cos(y(x))/(x*sin(y(x))-1)*(x-cos(y(x))+1)/(1+x);
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= \arctan \left (\frac {\left (-\ln \left (x +1\right )+c_{1} \right ) \sqrt {\ln \left (x +1\right )^{2}-2 c_{1} \ln \left (x +1\right )+c_{1}^{2}-x^{2}+1}+x}{c_{1}^{2}-2 c_{1} \ln \left (x +1\right )+\ln \left (x +1\right )^{2}+1}, \frac {\ln \left (x +1\right ) x -c_{1} x +\sqrt {\ln \left (x +1\right )^{2}-2 c_{1} \ln \left (x +1\right )+c_{1}^{2}-x^{2}+1}}{c_{1}^{2}-2 c_{1} \ln \left (x +1\right )+\ln \left (x +1\right )^{2}+1}\right ) \\
y &= \arctan \left (\frac {\left (\ln \left (x +1\right )-c_{1} \right ) \sqrt {\ln \left (x +1\right )^{2}-2 c_{1} \ln \left (x +1\right )+c_{1}^{2}-x^{2}+1}+x}{c_{1}^{2}-2 c_{1} \ln \left (x +1\right )+\ln \left (x +1\right )^{2}+1}, \frac {\ln \left (x +1\right ) x -c_{1} x -\sqrt {\ln \left (x +1\right )^{2}-2 c_{1} \ln \left (x +1\right )+c_{1}^{2}-x^{2}+1}}{c_{1}^{2}-2 c_{1} \ln \left (x +1\right )+\ln \left (x +1\right )^{2}+1}\right ) \\
\end{align*}
✓ Mathematica. Time used: 61.801 (sec). Leaf size: 221
ode=D[y[x],x] == -(((1 + x - Cos[y[x]])*Cos[y[x]])/((1 + x)*(-1 + x*Sin[y[x]])));
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to -\sec ^{-1}\left (\frac {-\sqrt {-x^2+\log ^2(x+1)+2 c_1 \log (x+1)+1+c_1{}^2}+x \log (x+1)+c_1 x}{x^2-1}\right ) \\
y(x)\to \sec ^{-1}\left (\frac {-\sqrt {-x^2+\log ^2(x+1)+2 c_1 \log (x+1)+1+c_1{}^2}+x \log (x+1)+c_1 x}{x^2-1}\right ) \\
y(x)\to -\sec ^{-1}\left (\frac {\sqrt {-x^2+\log ^2(x+1)+2 c_1 \log (x+1)+1+c_1{}^2}+x \log (x+1)+c_1 x}{x^2-1}\right ) \\
y(x)\to \sec ^{-1}\left (\frac {\sqrt {-x^2+\log ^2(x+1)+2 c_1 \log (x+1)+1+c_1{}^2}+x \log (x+1)+c_1 x}{x^2-1}\right ) \\
\end{align*}
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(Derivative(y(x), x) + (x - cos(y(x)) + 1)*cos(y(x))/((x + 1)*(x*sin(y(x)) - 1)),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out