73.7.9 problem 9

Internal problem ID [15088]
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 : 9
Date solved : Thursday, March 13, 2025 at 05:37:12 AM
CAS classification : [[_homogeneous, `class G`], _exact, _rational, _Bernoulli]

\begin{align*} x y^{2}-6+x^{2} y y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 30

ode:=x*y(x)^2-6+x^2*y(x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {\sqrt {12 x +c_{1}}}{x} \\ y &= -\frac {\sqrt {12 x +c_{1}}}{x} \\ \end{align*}

✓ Mathematica. Time used: 0.179 (sec). Leaf size: 38

ode=x*y[x]^2-6+x^2*y[x]*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {\sqrt {12 x+c_1}}{x} \\ y(x)\to \frac {\sqrt {12 x+c_1}}{x} \\ \end{align*}

✓ Sympy. Time used: 0.383 (sec). Leaf size: 26

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

\[ \left [ y{\left (x \right )} = - \frac {\sqrt {C_{1} + 12 x}}{x}, \ y{\left (x \right )} = \frac {\sqrt {C_{1} + 12 x}}{x}\right ] \]