12.5.36 problem 33

Internal problem ID [1660]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number : 33
Date solved : Thursday, March 13, 2025 at 04:22:35 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Maple. Time used: 2.000 (sec). Leaf size: 129

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

\[ y = x \left (\operatorname {RootOf}\left (x^{2} c_1 \,\textit {\_Z}^{8}+2 x^{2} c_1 \,\textit {\_Z}^{6}+c_1 \,\textit {\_Z}^{4} x^{2}-2 \textit {\_Z}^{2}-1\right )^{6} c_1 \,x^{2}+2 \operatorname {RootOf}\left (x^{2} c_1 \,\textit {\_Z}^{8}+2 x^{2} c_1 \,\textit {\_Z}^{6}+c_1 \,\textit {\_Z}^{4} x^{2}-2 \textit {\_Z}^{2}-1\right )^{4} c_1 \,x^{2}+\operatorname {RootOf}\left (x^{2} c_1 \,\textit {\_Z}^{8}+2 x^{2} c_1 \,\textit {\_Z}^{6}+c_1 \,\textit {\_Z}^{4} x^{2}-2 \textit {\_Z}^{2}-1\right )^{2} c_1 \,x^{2}-1\right ) \]

✓ Mathematica. Time used: 60.17 (sec). Leaf size: 1989

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

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

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

Timed Out