73.7.43 problem 43

Internal problem ID [15130]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 43
Date solved : Monday, March 31, 2025 at 01:26:32 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=y^{3}-y^{3} \cos \left (x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 31

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

\begin{align*} y &= \frac {1}{\sqrt {c_1 -2 x +2 \sin \left (x \right )}} \\ y &= -\frac {1}{\sqrt {c_1 -2 x +2 \sin \left (x \right )}} \\ \end{align*}

✓ Mathematica. Time used: 0.179 (sec). Leaf size: 77

ode=D[y[x],x]==y[x]^3-y[x]^3*Cos[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {1}{\sqrt {2} \sqrt {-\int _1^x(1-\cos (K[1]))dK[1]-c_1}} \\ y(x)\to \frac {1}{\sqrt {2} \sqrt {-\int _1^x(1-\cos (K[1]))dK[1]-c_1}} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.982 (sec). Leaf size: 46

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

\[ \left [ y{\left (x \right )} = - \frac {\sqrt {2} \sqrt {- \frac {1}{C_{1} + x - \sin {\left (x \right )}}}}{2}, \ y{\left (x \right )} = \frac {\sqrt {2} \sqrt {- \frac {1}{C_{1} + x - \sin {\left (x \right )}}}}{2}\right ] \]