1.5 problem 1(e)

Internal problem ID [2524]

Book: Elementary Differential equations, Chaundy, 1969
Section: Exercises 3, page 60
Problem number: 1(e).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

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

Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

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

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

Solution by Mathematica

Time used: 0.065 (sec). Leaf size: 27

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

\begin{align*} y(x)\to \cos (x) \left (\log \left (\sin \left (\frac {x}{2}\right )\right )-\log \left (\cos \left (\frac {x}{2}\right )\right )+c_1\right ) \\ \end{align*}