73.4.9 problem 5.1 (i)

Internal problem ID [15012]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page 103
Problem number : 5.1 (i)
Date solved : Thursday, March 13, 2025 at 05:26:48 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+4 y&=y^{3} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 33

ode:=diff(y(x),x)+4*y(x) = y(x)^3; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {2}{\sqrt {4 \,{\mathrm e}^{8 x} c_{1} +1}} \\ y &= \frac {2}{\sqrt {4 \,{\mathrm e}^{8 x} c_{1} +1}} \\ \end{align*}

✓ Mathematica. Time used: 0.22 (sec). Leaf size: 51

ode=D[y[x],x]+4*y[x]==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]-2) K[1] (K[1]+2)}dK[1]\&\right ][x+c_1] \\ y(x)\to -2 \\ y(x)\to 0 \\ y(x)\to 2 \\ \end{align*}

✓ Sympy. Time used: 1.163 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)**3 + 4*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - 2 \sqrt {\frac {C_{1}}{C_{1} - e^{8 x}}}, \ y{\left (x \right )} = 2 \sqrt {\frac {C_{1}}{C_{1} - e^{8 x}}}\right ] \]