6.1 problem Ex 1

Internal problem ID [10129]

Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 13. Linear equations of first order. Page 19
Problem number: Ex 1.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {y^{\prime }+\cot \relax (x ) y-\sec \relax (x )=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 16

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

\[ y \relax (x ) = \frac {-\ln \left (\cos \relax (x )\right )+c_{1}}{\sin \relax (x )} \]

Solution by Mathematica

Time used: 0.066 (sec). Leaf size: 16

DSolve[y'[x]+y[x]*Cot[x]==Sec[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \csc (x) (-\log (\cos (x))+c_1) \\ \end{align*}