54.2.309 problem 888

Internal problem ID [12183]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 888
Date solved : Wednesday, October 01, 2025 at 01:06:53 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class C`], [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} y^{\prime }&=\frac {6 x^{2} y-2 x +1-5 x^{3} y^{2}-2 x y+y^{3} x^{4}}{x^{2} \left (x^{2} y-x +1\right )} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 85

ode:=diff(y(x),x) = 1/x^2*(6*x^2*y(x)-2*x+1-5*x^3*y(x)^2-2*x*y(x)+y(x)^3*x^4)/(x^2*y(x)-x+1); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.496 (sec). Leaf size: 74

ode=D[y[x],x] == (1 - 2*x - 2*x*y[x] + 6*x^2*y[x] - 5*x^3*y[x]^2 + x^4*y[x]^3)/(x^2*(1 - x + x^2*y[x])); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x-1}{x^2}+\frac {1}{x^4 \left (\frac {1}{x^2}-\frac {1}{x^2 \sqrt {\frac {2}{x}+c_1}}\right )}\\ y(x)&\to \frac {x+\frac {1}{1+\frac {1}{\sqrt {\frac {2}{x}+c_1}}}-1}{x^2}\\ y(x)&\to \frac {1}{x} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (x**4*y(x)**3 - 5*x**3*y(x)**2 + 6*x**2*y(x) - 2*x*y(x) - 2*x + 1)/(x**2*(x**2*y(x) - x + 1)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out