Internal problem ID [2533]
Book: Elementary Differential equations, Chaundy, 1969
Section: Exercises 3, page 60
Problem number: 3(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } \tan \relax (x )+y-\cot \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 21
dsolve(tan(x)*diff(y(x),x)+y(x)=cot(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\cos \relax (x )+\ln \left (\csc \relax (x )-\cot \relax (x )\right )+c_{1}}{\sin \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.066 (sec). Leaf size: 29
DSolve[Tan[x]*y'[x]+y[x]==Cot[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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 ) \\ \end{align*}