60.2.422 problem 1000

Internal problem ID [10996]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 1000
Date solved : Sunday, March 30, 2025 at 07:38:35 PM
CAS classification : [_Riccati]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 19

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

\[ y = \frac {x \left (c_1 x -1\right )}{\ln \left (x \right ) c_1 +1} \]

✓ Mathematica. Time used: 1.103 (sec). Leaf size: 27

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

\begin{align*} y(x)\to \frac {x (x-c_1)}{\log (x)+c_1} \\ y(x)\to -x \\ \end{align*}

✗ Sympy

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

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