60.2.178 problem 754

Internal problem ID [10752]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 754
Date solved : Wednesday, March 05, 2025 at 12:35:40 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Abel]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 26

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

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

✓ Mathematica. Time used: 0.09 (sec). Leaf size: 32

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

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

✗ Sympy

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

Timed Out