67.5.9 problem 6.5 (a)

Internal problem ID [16407]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number : 6.5 (a)
Date solved : Thursday, October 02, 2025 at 01:28:55 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+3 y&=3 y^{3} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 29

ode:=diff(y(x),x)+3*y(x) = 3*y(x)^3; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {1}{\sqrt {{\mathrm e}^{6 x} c_1 +1}} \\ y &= -\frac {1}{\sqrt {{\mathrm e}^{6 x} c_1 +1}} \\ \end{align*}

✓ Mathematica. Time used: 0.123 (sec). Leaf size: 53

ode=D[y[x],x]+3*y[x]==3*y[x]^3; 
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]-1) K[1] (K[1]+1)}dK[1]\&\right ][3 x+c_1]\\ y(x)&\to -1\\ y(x)&\to 0\\ y(x)&\to 1 \end{align*}

✓ Sympy. Time used: 0.754 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*y(x)**3 + 3*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \sqrt {\frac {C_{1}}{C_{1} - e^{6 x}}}, \ y{\left (x \right )} = \sqrt {\frac {C_{1}}{C_{1} - e^{6 x}}}\right ] \]