67.3.13 problem 4.4 (c)

Internal problem ID [16334]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.4 (c)
Date solved : Thursday, October 02, 2025 at 01:20:53 PM
CAS classification : [_separable]

\begin{align*} x y y^{\prime }&=y^{2}+9 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

ode:=x*y(x)*diff(y(x),x) = y(x)^2+9; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \sqrt {c_1 \,x^{2}-9} \\ y &= -\sqrt {c_1 \,x^{2}-9} \\ \end{align*}

✓ Mathematica. Time used: 0.237 (sec). Leaf size: 57

ode=x*y[x]*D[y[x],x]==y[x]^2+9; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt {-9+e^{2 c_1} x^2}\\ y(x)&\to \sqrt {-9+e^{2 c_1} x^2}\\ y(x)&\to -3 i\\ y(x)&\to 3 i \end{align*}

✓ Sympy. Time used: 0.282 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*y(x)*Derivative(y(x), x) - y(x)**2 - 9,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \sqrt {C_{1} x^{2} - 9}, \ y{\left (x \right )} = \sqrt {C_{1} x^{2} - 9}\right ] \]