24.1.14 problem 3(c)

Internal problem ID [4203]
Book : Elementary Differential equations, Chaundy, 1969
Section : Exercises 3, page 60
Problem number : 3(c)
Date solved : Monday, January 27, 2025 at 08:42:04 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.066 (sec). Leaf size: 29

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

\[ y(x)\to \csc (x) \left (\cos (x)+\log \left (\sin \left (\frac {x}{2}\right )\right )-\log \left (\cos \left (\frac {x}{2}\right )\right )+c_1\right ) \]