1.5 problem 1(e)

Internal problem ID [3033]

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]

\[ \boxed {y^{\prime }+y \tan \left (x \right )=\cot \left (x \right )} \]

✓ Solution by Maple

Time used: 0.0 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.058 (sec). Leaf size: 16

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

\[ y(x)\to \cos (x) (-\text {arctanh}(\cos (x))+c_1) \]