68.7.47 problem 47

Internal problem ID [17411]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 47
Date solved : Sunday, October 12, 2025 at 05:33:11 AM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }+y \cot \left (x \right )&=y^{4} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 5

ode:=diff(y(x),x)+y(x)*cot(x) = y(x)^4; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 0 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 6

ode=D[y[x],x]+y[x]*Cot[x]==y[x]^4; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 0 \end{align*}

✗ Sympy

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