73.2.3 problem 3.4 c

Internal problem ID [14947]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 3. Some basics about First order equations. Additional exercises. page 63
Problem number : 3.4 c
Date solved : Thursday, March 13, 2025 at 05:22:10 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-y^{3}&=8 \end{align*}

✓ Maple. Time used: 1.142 (sec). Leaf size: 50

ode:=diff(y(x),x)-y(x)^3 = 8; 
dsolve(ode,y(x), singsol=all);
 

\[ y = 1+\sqrt {3}\, \tan \left (\operatorname {RootOf}\left (-\sqrt {3}\, \ln \left (\cos \left (\textit {\_Z} \right )^{2}\right )-2 \sqrt {3}\, \ln \left (\tan \left (\textit {\_Z} \right )+\sqrt {3}\right )+24 \sqrt {3}\, c_{1} +24 \sqrt {3}\, x -6 \textit {\_Z} \right )\right ) \]

✓ Mathematica. Time used: 0.202 (sec). Leaf size: 65

ode=D[y[x],x]-y[x]^3==8; 
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) \left (K[1]^2-2 K[1]+4\right )}dK[1]\&\right ][x+c_1] \\ y(x)\to -2 \\ y(x)\to 2 \sqrt [3]{-1} \\ y(x)\to -2 (-1)^{2/3} \\ \end{align*}

✓ Sympy. Time used: 0.629 (sec). Leaf size: 46

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)**3 + Derivative(y(x), x) - 8,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ x - \frac {\log {\left (y{\left (x \right )} + 2 \right )}}{12} + \frac {\log {\left (y^{2}{\left (x \right )} - 2 y{\left (x \right )} + 4 \right )}}{24} - \frac {\sqrt {3} \operatorname {atan}{\left (\frac {\sqrt {3} \left (y{\left (x \right )} - 1\right )}{3} \right )}}{12} = C_{1} \]