60.2.128 problem 704

Internal problem ID [10702]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 704
Date solved : Wednesday, March 05, 2025 at 12:21:24 PM
CAS classification : [[_homogeneous, `class D`], _Riccati]

\begin{align*} y^{\prime }&=\frac {y \ln \left (x \right ) x -y+2 x^{5} b +2 x^{3} a y^{2}}{\left (x \ln \left (x \right )-1\right ) x} \end{align*}

✓ Maple. Time used: 0.068 (sec). Leaf size: 38

ode:=diff(y(x),x) = (y(x)*ln(x)*x-y(x)+2*x^5*b+2*x^3*a*y(x)^2)/(x*ln(x)-1)/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\tan \left (2 \sqrt {a b}\, \left (\int \frac {x^{3}}{\ln \left (x \right ) x -1}d x +c_{1} \right )\right ) x \sqrt {a b}}{a} \]

✓ Mathematica. Time used: 0.228 (sec). Leaf size: 52

ode=D[y[x],x] == (2*b*x^5 - y[x] + x*Log[x]*y[x] + 2*a*x^3*y[x]^2)/(x*(-1 + x*Log[x])); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{a K[1]^2+b}dK[1]=\int _1^x\frac {2 K[2]^3}{K[2] \log (K[2])-1}dK[2]+c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (2*a*x**3*y(x)**2 + 2*b*x**5 + x*y(x)*log(x) - y(x))/(x*(x*log(x) - 1)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (2*a*x**3*y(x)**2 + 2*b*x**5 + x*y(x)*log(x) - y(x))/(x*(x*log(x) - 1)) cannot be solved by the lie group method