2.39 problem 39

Internal problem ID [6724]

Book: Second order enumerated odes
Section: section 2
Problem number: 39.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {y^{\prime }+y \cot \relax (x )-2 \cos \relax (x )=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 17

dsolve(diff(y(x),x)+y(x)*cot(x)=2*cos(x),y(x), singsol=all)
 

\[ y \relax (x ) = \frac {-\frac {\cos \left (2 x \right )}{2}+c_{1}}{\sin \relax (x )} \]

Solution by Mathematica

Time used: 0.091 (sec). Leaf size: 17

DSolve[y'[x]+y[x]*Cot[x]==2*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \sin (x)+\left (-\frac {1}{2}+c_1\right ) \csc (x) \\ \end{align*}