67.5.10 problem 6.5 (b)

Internal problem ID [16408]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number : 6.5 (b)
Date solved : Thursday, October 02, 2025 at 01:28:56 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} y^{\prime }-\frac {3 y}{x}&=\frac {y^{2}}{x^{2}} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

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

\[ y = -\frac {2 x^{3}}{x^{2}-2 c_1} \]

✓ Mathematica. Time used: 0.096 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to -\frac {2 x^3}{x^2-2 c_1}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.124 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = \frac {2 x^{3}}{C_{1} - x^{2}} \]