60.2.355 problem 933

Internal problem ID [10929]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 933
Date solved : Sunday, March 30, 2025 at 07:25:30 PM
CAS classification : [_Abel]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 39

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

\[ y = \frac {x \left (9 \ln \left (x \right )-3+29 \operatorname {RootOf}\left (-81 \int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} +x +3 c_1 \right )\right )}{9} \]

✓ Mathematica. Time used: 1.229 (sec). Leaf size: 77

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

\[ \text {Solve}\left [\int _1^{\frac {\frac {1-3 \log (x)}{x}+\frac {3 y(x)}{x^2}}{\sqrt [3]{29} \sqrt [3]{\frac {1}{x^3}}}}\frac {1}{K[1]^3-\frac {3 K[1]}{29^{2/3}}+1}dK[1]=\frac {29^{2/3}}{9 \sqrt [3]{\frac {1}{x^3}}}+c_1,y(x)\right ] \]

✗ Sympy

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

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