29.21.10 problem 586

Internal problem ID [5180]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 21
Problem number : 586
Date solved : Tuesday, March 04, 2025 at 08:24:35 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x \left (3+2 x^{2} y\right ) y^{\prime }+\left (4+3 x^{2} y\right ) y&=0 \end{align*}

✓ Maple. Time used: 2.017 (sec). Leaf size: 39

ode:=x*(3+2*x^2*y(x))*diff(y(x),x)+(4+3*x^2*y(x))*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {\operatorname {RootOf}\left (x^{2} \textit {\_Z}^{8}-2 \textit {\_Z}^{2} c_{1} -c_{1} \right )^{6} x^{2}-2 c_{1}}{x^{2} c_{1}} \]

✓ Mathematica. Time used: 60.317 (sec). Leaf size: 1769

ode=x(3+2 x^2 y[x])D[y[x],x]+(4+3 x^2 y[x])y[x]==0; 
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*(2*x**2*y(x) + 3)*Derivative(y(x), x) + (3*x**2*y(x) + 4)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out