60.2.337 problem 915

Internal problem ID [10911]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 915
Date solved : Sunday, March 30, 2025 at 07:22:32 PM
CAS classification : [[_Abel, `2nd type`, `class C`]]

\begin{align*} y^{\prime }&=-\frac {-y^{3}-y+4 y^{2} \ln \left (x \right )-4 \ln \left (x \right )^{2} y^{3}-1+6 y \ln \left (x \right )-12 \ln \left (x \right )^{2} y^{2}+8 \ln \left (x \right )^{3} y^{3}}{y x} \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 43

ode:=diff(y(x),x) = -(-y(x)^3-y(x)+4*y(x)^2*ln(x)-4*ln(x)^2*y(x)^3-1+6*y(x)*ln(x)-12*ln(x)^2*y(x)^2+8*ln(x)^3*y(x)^3)/y(x)/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {9}{18 \ln \left (x \right )+83 \operatorname {RootOf}\left (-81 \int _{}^{\textit {\_Z}}\frac {1}{6889 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} -\ln \left (x \right )+3 c_1 \right )-3} \]

✓ Mathematica. Time used: 0.273 (sec). Leaf size: 71

ode=D[y[x],x] == (1 + y[x] - 6*Log[x]*y[x] - 4*Log[x]*y[x]^2 + 12*Log[x]^2*y[x]^2 + y[x]^3 + 4*Log[x]^2*y[x]^3 - 8*Log[x]^3*y[x]^3)/(x*y[x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{\frac {(-1)^{2/3} (-6 \log (x) y(x)+y(x)+3)}{\sqrt [3]{83} y(x)}}\frac {1}{K[1]^3+\frac {3 \sqrt [3]{-1} K[1]}{83^{2/3}}+1}dK[1]+\frac {1}{9} (-83)^{2/3} \log (x)=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) + (8*y(x)**3*log(x)**3 - 4*y(x)**3*log(x)**2 - y(x)**3 - 12*y(x)**2*log(x)**2 + 4*y(x)**2*log(x) + 6*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) - ((-8*y(x)**2*log(x)**3 + 4*y(x)**2*log(x)**2 + y(x)**2 + 12*y(x)*log(x)**2 - 4*y(x)*log(x) - 6*log(x) + 1)*y(x) + 1)/(x*y(x)) cannot be solved by the factorable group method