67.6.13 problem 7.5 (c)

Internal problem ID [16439]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 7. The exact form and general integrating fators. Additional exercises. page 141
Problem number : 7.5 (c)
Date solved : Thursday, October 02, 2025 at 01:33:10 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 1.508 (sec). Leaf size: 28

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

\[ y = \frac {\operatorname {RootOf}\left (c_1 \,\textit {\_Z}^{32}-c_1 \,\textit {\_Z}^{24}-x^{8}\right )^{8}}{x^{2}} \]

✓ Mathematica. Time used: 60.165 (sec). Leaf size: 1985

ode=2*y[x]/x+(4*x^2*y[x]-3)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✓ Sympy. Time used: 145.294 (sec). Leaf size: 1231

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((4*x**2*y(x) - 3)*Derivative(y(x), x) + 2*y(x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \text {Solution too large to show} \]