Internal problem ID [1984]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number: Problem 14.5 (b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-\cot \relax (x ) y+\frac {1}{\sin \relax (x )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 13
dsolve(diff(y(x),x)-y(x)*cot(x)+1/sin(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \left (\frac {1}{\tan \relax (x )}+c_{1}\right ) \sin \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 13
DSolve[y'[x]-y[x]*Cot[x]+1/Sin[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \cos (x)+c_1 \sin (x) \\ \end{align*}