60.2.408 problem 986

Internal problem ID [10982]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 986
Date solved : Sunday, March 30, 2025 at 07:37:04 PM
CAS classification : [_Abel]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 40

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

\begin{align*} y &= x \ln \left (x \right ) \\ y &= x \left (-\frac {1}{\sqrt {c_1 -2 x}}+\ln \left (x \right )\right ) \\ y &= x \left (\frac {1}{\sqrt {c_1 -2 x}}+\ln \left (x \right )\right ) \\ \end{align*}

✓ Mathematica. Time used: 0.248 (sec). Leaf size: 49

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

\begin{align*} y(x)\to x \left (\log (x)-\frac {1}{\sqrt {-2 x+c_1}}\right ) \\ y(x)\to x \left (\log (x)+\frac {1}{\sqrt {-2 x+c_1}}\right ) \\ y(x)\to x \log (x) \\ \end{align*}

✗ Sympy

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

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