54.2.265 problem 843

Internal problem ID [12139]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 843
Date solved : Wednesday, October 01, 2025 at 12:58:18 AM
CAS classification : [_Riccati]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 43

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

\[ y = -\frac {\ln \left (x \right ) \left (6 x^{3} \ln \left (x \right )-2 x^{3}+9 c_1 +18\right )}{6 x^{3} \ln \left (x \right )-2 x^{3}+9 c_1} \]

✓ Mathematica. Time used: 0.208 (sec). Leaf size: 52

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

\begin{align*} y(x)&\to \frac {\log (x) \left (x^3-3 x^3 \log (x)-9 (1+c_1)\right )}{-x^3+3 x^3 \log (x)+9 c_1}\\ y(x)&\to -\log (x) \end{align*}

✗ Sympy

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

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