54.2.326 problem 905

Internal problem ID [12200]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 905
Date solved : Wednesday, October 01, 2025 at 01:08:43 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Abel]

\begin{align*} y^{\prime }&=\frac {a^{2} x +a^{3} x^{3}+a^{3} x^{3} y^{2}+2 a^{2} x^{2} y+a x +y^{3} a^{3} x^{3}+3 y^{2} a^{2} x^{2}+3 y a x +1}{a^{3} x^{3}} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 46

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

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

✓ Mathematica. Time used: 0.127 (sec). Leaf size: 63

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

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

✗ Sympy

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

Timed Out