73.6.13 problem 7.5 (c)

Internal problem ID [15081]
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 : Monday, March 31, 2025 at 01:22:53 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: 2.056 (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: 0.21 (sec). Leaf size: 77

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]
 

\[ \text {Solve}\left [\int _1^{\frac {(-1)^{2/3} \left (8 x^2 y(x)-15\right )}{\sqrt [3]{70} \left (4 x^2 y(x)-3\right )}}\frac {1}{K[1]^3+\frac {39 \sqrt [3]{-1} K[1]}{70^{2/3}}+1}dK[1]=\frac {2}{27} (-70)^{2/3} \log (x)+c_1,y(x)\right ] \]

✗ Sympy

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)
 

Timed Out