Internal problem ID [14082]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=\cos \left (x \right ) \cot \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(y(x),x)=cos(x)*cot(x),y(x), singsol=all)
\[ y \left (x \right ) = \cos \left (x \right )+\ln \left (\csc \left (x \right )-\cot \left (x \right )\right )+c_{1} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 26
DSolve[y'[x]==Cos[x]*Cot[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \cos (x)+\log \left (\sin \left (\frac {x}{2}\right )\right )-\log \left (\cos \left (\frac {x}{2}\right )\right )+c_1 \]