73.7.2 problem 2

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 8. Review exercises for part of part II. page 143
Problem number : 2
Date solved : Thursday, March 13, 2025 at 05:36:44 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (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: 0.241 (sec). Leaf size: 43

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 \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-3) K[1]}dK[1]\&\right ][2 \log (x)+c_1] \\ y(x)\to 0 \\ y(x)\to 3 \\ \end{align*}

✓ Sympy. Time used: 0.325 (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)
 

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