67.1.19 problem 2.3 (i)

Internal problem ID [16284]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.3 (i)
Date solved : Thursday, October 02, 2025 at 10:45:20 AM
CAS classification : [_quadrature]

\begin{align*} 1&=x^{2}-9 y^{\prime } \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=1 = x^2-9*diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{27} x^{3}-\frac {1}{9} x +c_1 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 20

ode=1==x^2-9*D[y[x],x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^3}{27}-\frac {x}{9}+c_1 \end{align*}

✓ Sympy. Time used: 0.076 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2 + 9*Derivative(y(x), x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + \frac {x^{3}}{27} - \frac {x}{9} \]