67.3.23 problem 4.6 (c)

Internal problem ID [16344]
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 : 4.6 (c)
Date solved : Thursday, October 02, 2025 at 01:21:14 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 29

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

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

✓ Mathematica. Time used: 1.774 (sec). Leaf size: 53

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

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

✓ Sympy. Time used: 0.354 (sec). Leaf size: 29

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

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