32.4.8 problem Recognizable Exact Differential equations. Integrating factors. Example 10.83, page 90

Internal problem ID [5819]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 10
Problem number : Recognizable Exact Differential equations. Integrating factors. Example 10.83, page 90
Date solved : Sunday, March 30, 2025 at 10:18:42 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} y \left (2 x^{2} y^{3}+3\right )+x \left (x^{2} y^{3}-1\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.035 (sec). Leaf size: 39

ode:=y(x)*(2*x^2*y(x)^3+3)+x*(x^2*y(x)^3-1)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{-\frac {11 c_1}{3}} x^{3}}{\operatorname {RootOf}\left (11 \,{\mathrm e}^{11 c_1} \textit {\_Z}^{15}-{\mathrm e}^{11 c_1} \textit {\_Z}^{11}+4 x^{11}\right )^{5}} \]

✓ Mathematica. Time used: 11.496 (sec). Leaf size: 1081

ode=(y[x]*(2*x^2*y[x]^3+3))+(x*(x^2*y[x]^3-1))*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.867 (sec). Leaf size: 34

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

\[ - \log {\left (x \right )} + \frac {3 \log {\left (x^{\frac {2}{3}} y{\left (x \right )} \right )}}{11} - \frac {15 \log {\left (4 x^{2} y^{3}{\left (x \right )} + 11 \right )}}{44} = C_{1} \]