60.2.416 problem 994

Internal problem ID [10990]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 994
Date solved : Wednesday, March 05, 2025 at 01:35:36 PM
CAS classification : [_Riccati]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 43

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

\[ y = -\frac {\ln \left (x \right ) \left (4 \ln \left (x \right ) x^{4}-x^{4}+8 c_{1} +16\right )}{4 \ln \left (x \right ) x^{4}-x^{4}+8 c_{1}} \]

✓ Mathematica. Time used: 0.339 (sec). Leaf size: 52

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

\begin{align*} y(x)\to \frac {\log (x) \left (x^4-4 x^4 \log (x)-16 (1+c_1)\right )}{-x^4+4 x^4 \log (x)+16 c_1} \\ y(x)\to -\log (x) \\ \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (x**4*(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