54.2.274 problem 852

Internal problem ID [12148]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 852
Date solved : Wednesday, October 01, 2025 at 01:00:50 AM
CAS classification : [[_homogeneous, `class C`], _Abel]

\begin{align*} y^{\prime }&=\frac {\alpha ^{3}+y^{2} \alpha ^{3}+2 y \alpha ^{2} \beta x +\alpha \,\beta ^{2} x^{2}+y^{3} \alpha ^{3}+3 y^{2} \alpha ^{2} \beta x +3 y \alpha \,\beta ^{2} x^{2}+\beta ^{3} x^{3}}{\alpha ^{3}} \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 42

ode:=diff(y(x),x) = (alpha^3+y(x)^2*alpha^3+2*y(x)*alpha^2*beta*x+alpha*beta^2*x^2+y(x)^3*alpha^3+3*y(x)^2*alpha^2*beta*x+3*y(x)*alpha*beta^2*x^2+beta^3*x^3)/alpha^3; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.137 (sec). Leaf size: 92

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

\[ \text {Solve}\left [\int _1^{\frac {\frac {\alpha +3 x \beta }{\alpha }+3 y(x)}{\sqrt [3]{\frac {29 \alpha +27 \beta }{\alpha }}}}\frac {1}{K[1]^3-\frac {3 \alpha ^{2/3} K[1]}{(29 \alpha +27 \beta )^{2/3}}+1}dK[1]=\frac {1}{9} x \left (\frac {29 \alpha +27 \beta }{\alpha }\right )^{2/3}+c_1,y(x)\right ] \]

✗ Sympy

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

TypeError : argument of type Mul is not iterable