Internal problem ID [2532]
Book: Elementary Differential equations, Chaundy, 1969
Section: Exercises 3, page 60
Problem number: 3(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\cot \relax (x ) y^{\prime }+y-\tan \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(cot(x)*diff(y(x),x)+y(x)=tan(x),y(x), singsol=all)
\[ y \relax (x ) = \left (-\frac {\ln \left (\sec \relax (x )+\tan \relax (x )\right )}{2}+\frac {\sec \relax (x ) \tan \relax (x )}{2}+c_{1}\right ) \cos \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.075 (sec). Leaf size: 25
DSolve[Cot[x]*y'[x]+y[x]==Tan[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (\tan (x)+2 c_1 \cos (x)+\cos (x) \left (-\tanh ^{-1}(\sin (x))\right )\right ) \\ \end{align*}