60.2.149 problem 725

Internal problem ID [10723]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 725
Date solved : Wednesday, March 05, 2025 at 12:28:42 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

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

\[ y = -x -\tan \left (c_{1} -x +\ln \left (2\right ) \operatorname {Ei}_{1}\left (-\ln \left (x \right )\right )\right ) \]

✓ Mathematica. Time used: 0.536 (sec). Leaf size: 31

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

\[ y(x)\to -x+\tan \left (\int _1^x\frac {\log (2 K[5])}{\log (K[5])}dK[5]+c_1\right ) \]

✗ Sympy

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

NotImplementedError : The given ODE -(x**2*log(2) + x*y(x)*log(4) + (x**2 + 2*x*y(x) + y(x)**2)*log(x) + y(x)**2*log(2) + log(2))/log(x) + Derivative(y(x), x) cannot be solved by the factorable group method