67.7.2 problem 2

Internal problem ID [16447]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 2
Date solved : Thursday, October 02, 2025 at 01:33:29 PM
CAS classification : [_separable]

\begin{align*} x y^{\prime }&=2 y^{2}-6 y \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=x*diff(y(x),x) = 2*y(x)^2-6*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {3}{3 c_1 \,x^{6}+1} \]

✓ Mathematica. Time used: 1.795 (sec). Leaf size: 31

ode=x*D[y[x],x]==2*y[x]^2-6*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {3}{1+e^{3 c_1} x^6}\\ y(x)&\to 0\\ y(x)&\to 3 \end{align*}

✓ Sympy. Time used: 0.187 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) - 2*y(x)**2 + 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {3}{C_{1} x^{6} - 1} \]