54.2.223 problem 800

Internal problem ID [12097]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 800
Date solved : Wednesday, October 01, 2025 at 12:32:16 AM
CAS classification : [[_homogeneous, `class C`], _rational, _Abel]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 41

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

\[ y = \frac {\operatorname {RootOf}\left (-\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3}-\textit {\_a}^{2}-\textit {\_a} -1}d \textit {\_a} +\ln \left (-2 x +b \right )+c_1 \right ) \left (-2 x +b \right )}{2} \]

✓ Mathematica. Time used: 0.247 (sec). Leaf size: 109

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

\[ \text {Solve}\left [\int _1^{\frac {\frac {4}{(b-2 x)^2}-\frac {24 y(x)}{(b-2 x)^3}}{4 \sqrt [3]{38} \sqrt [3]{\frac {1}{(b-2 x)^6}}}}\frac {1}{K[1]^3-\frac {6 \sqrt [3]{2} K[1]}{19^{2/3}}+1}dK[1]=\frac {1}{9} 38^{2/3} \left (\frac {1}{(b-2 x)^6}\right )^{2/3} (b-2 x)^4 \log (b-2 x)+c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
b = symbols("b") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (-b**3 + 6*b**2*x - 12*b*x**2 - 4*b*y(x)**2 + 8*x**3 + 8*x*y(x)**2 + 8*y(x)**3)/(-b + 2*x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

TypeError : argument of type Mul is not iterable