24.1.5 problem 1(e)

Internal problem ID [4194]
Book : Elementary Differential equations, Chaundy, 1969
Section : Exercises 3, page 60
Problem number : 1(e)
Date solved : Monday, January 27, 2025 at 08:41:45 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (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: 0.046 (sec). Leaf size: 16

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

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