67.3.12 problem 4.4 (b)

Internal problem ID [16333]
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 (b)
Date solved : Thursday, October 02, 2025 at 01:20:48 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 14

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

\[ y = 3 \tan \left (3 x +3 c_1 \right ) \]

✓ Mathematica. Time used: 0.105 (sec). Leaf size: 41

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

\begin{align*} y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1]^2+9}dK[1]\&\right ][x+c_1]\\ y(x)&\to -3 i\\ y(x)&\to 3 i \end{align*}

✓ Sympy. Time used: 0.156 (sec). Leaf size: 12

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

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