74.7.47 problem 47

Internal problem ID [16124]
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 : Tuesday, January 28, 2025 at 08:50:13 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*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 5

dsolve([diff(y(x),x)+y(x)*cot(x)=y(x)^4,y(0) = 0],y(x), singsol=all)
 

\[ y = 0 \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 6

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

\[ y(x)\to 0 \]