1.3 problem 1(c)

Internal problem ID [2522]

Book: Elementary Differential equations, Chaundy, 1969
Section: Exercises 3, page 60
Problem number: 1(c).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {y^{\prime }+\cot \relax (x ) y-x=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 18

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

\[ y \relax (x ) = \frac {\sin \relax (x )-x \cos \relax (x )+c_{1}}{\sin \relax (x )} \]

Solution by Mathematica

Time used: 0.061 (sec). Leaf size: 17

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

\begin{align*} y(x)\to -x \cot (x)+c_1 \csc (x)+1 \\ \end{align*}