54.2.170 problem 747

Internal problem ID [12044]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 747
Date solved : Wednesday, October 01, 2025 at 12:05:27 AM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }&=-\frac {y \left (\tan \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tan \left (x \right )} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 72

ode:=diff(y(x),x) = -y(x)*(tan(x)+ln(2*x)*x-ln(2*x)*x^2*y(x))/x/tan(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{-\int \frac {x \ln \left (2\right )+x \ln \left (x \right )+\tan \left (x \right )}{x \tan \left (x \right )}d x}}{-\int \frac {{\mathrm e}^{-\int \frac {x \ln \left (2\right )+x \ln \left (x \right )+\tan \left (x \right )}{x \tan \left (x \right )}d x} x \left (\ln \left (2\right )+\ln \left (x \right )\right )}{\tan \left (x \right )}d x +c_1} \]

✓ Mathematica. Time used: 0.578 (sec). Leaf size: 89

ode=D[y[x],x] == -((Cot[x]*y[x]*(x*Log[2*x] + Tan[x] - x^2*Log[2*x]*y[x]))/x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {\exp \left (\int _1^x\left (-\cot (K[1]) \log (2 K[1])-\frac {1}{K[1]}\right )dK[1]\right )}{-\int _1^x\exp \left (\int _1^{K[2]}\left (-\cot (K[1]) \log (2 K[1])-\frac {1}{K[1]}\right )dK[1]\right ) \cot (K[2]) K[2] \log (2 K[2])dK[2]+c_1}\\ y(x)&\to 0 \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) + (-x**2*y(x)*log(2*x) + x*log(2*x) + tan(x))*y(x)/(x*tan(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out