74.5.17 problem 17

Internal problem ID [15981]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 17
Date solved : Tuesday, January 28, 2025 at 08:25:33 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+2 y \cot \left (x \right )&=\cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

dsolve(diff(y(x),x)+2*y(x)*cot(x)=cos(x),y(x), singsol=all)
 

\[ y = \frac {\sin \left (x \right )}{3}+\csc \left (x \right )^{2} c_{1} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 19

DSolve[D[y[x],x]+2*y[x]*Cot[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sin (x)}{3}+c_1 \csc ^2(x) \]