74.5.13 problem 13

Internal problem ID [15977]
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 : 13
Date solved : Tuesday, January 28, 2025 at 08:25:22 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

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

\[ y = -\frac {\csc \left (t \right ) \left (2 \cos \left (t \right )^{2}-4 c_{1} -1\right )}{4} \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 19

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

\[ y(t)\to -\frac {1}{2} \cos (t) \cot (t)+c_1 \csc (t) \]