74.1.38 problem 45

Internal problem ID [15818]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 45
Date solved : Tuesday, January 28, 2025 at 08:08:07 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

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

\[ y = \cos \left (x \right )+\ln \left (\csc \left (x \right )-\cot \left (x \right )\right )+c_{1} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 22

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

\[ y(x)\to \int _1^x\cos (K[1]) \cot (K[1])dK[1]+c_1 \]