60.2.157 problem 733

Internal problem ID [10731]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 733
Date solved : Sunday, March 30, 2025 at 06:28:03 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

\begin{align*} y^{\prime }&=\frac {2 x \sin \left (x \right )-\ln \left (2 x \right )+\ln \left (2 x \right ) x^{4}-2 \ln \left (2 x \right ) x^{2} y+\ln \left (2 x \right ) y^{2}}{\sin \left (x \right )} \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 42

ode:=diff(y(x),x) = (2*x*sin(x)-ln(2*x)+ln(2*x)*x^4-2*ln(2*x)*x^2*y(x)+ln(2*x)*y(x)^2)/sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\int \left (\ln \left (2\right )+\ln \left (x \right )\right ) \csc \left (x \right )d x -2 i c_1} \operatorname {csch}\left (-\int \left (\ln \left (2\right )+\ln \left (x \right )\right ) \csc \left (x \right )d x +2 i c_1 \right )+x^{2}+1 \]

✓ Mathematica. Time used: 0.54 (sec). Leaf size: 82

ode=D[y[x],x] == Csc[x]*(-Log[2*x] + x^4*Log[2*x] + 2*x*Sin[x] - 2*x^2*Log[2*x]*y[x] + Log[2*x]*y[x]^2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {\exp \left (\int _1^x2 \csc (K[5]) \log (2 K[5])dK[5]\right )}{-\int _1^x\exp \left (\int _1^{K[6]}2 \csc (K[5]) \log (2 K[5])dK[5]\right ) \csc (K[6]) \log (2 K[6])dK[6]+c_1}+x^2+1 \\ y(x)\to x^2+1 \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-x**4*log(2*x) + 2*x**2*y(x)*log(2*x) - 2*x*sin(x) - y(x)**2*log(2*x) + log(2*x))/sin(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out