73.6.18 problem 7.5 (h)

Internal problem ID [15086]
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 (h)
Date solved : Monday, March 31, 2025 at 01:23:09 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 4 x y+\left (3 x^{2}+5 y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.219 (sec). Leaf size: 29

ode:=4*x*y(x)+(3*x^2+5*y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \operatorname {RootOf}\left (x^{5} \textit {\_Z}^{25}+x^{5} \textit {\_Z}^{15}-c_1 \right )^{10} x^{2} \]

✓ Mathematica. Time used: 60.071 (sec). Leaf size: 1121

ode=4*x*y[x]+(3*x^2+5*y[x])*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

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x*y(x) + (3*x**2 + 5*y(x))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE 4*x*y(x)/(3*x**2 + 5*y(x)) + Derivative(y(x), x) cannot be solved by the factorable group method