54.2.334 problem 913

Internal problem ID [12208]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 913
Date solved : Wednesday, October 01, 2025 at 01:13:30 AM
CAS classification : [[_Abel, `2nd type`, `class C`]]

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

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

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

\[ y = \frac {9}{9 \ln \left (x \right )+56 \operatorname {RootOf}\left (-81 \int _{}^{\textit {\_Z}}\frac {1}{3136 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} -\ln \left (x \right )+3 c_1 \right )-3} \]

✓ Mathematica. Time used: 0.154 (sec). Leaf size: 71

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

\[ \text {Solve}\left [\int _1^{\frac {(-1)^{2/3} \left (-3 \log (x)+\frac {3}{y(x)}+1\right )}{2 \sqrt [3]{7}}}\frac {28}{28 K[1]^3+3 \sqrt [3]{-7} K[1]+28}dK[1]+\frac {4}{9} (-7)^{2/3} \log (x)=c_1,y(x)\right ] \]

✗ Sympy

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

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