56.5.3 problem 3

Internal problem ID [8964]
Book : Own collection of miscellaneous problems
Section : section 5.0
Problem number : 3
Date solved : Monday, January 27, 2025 at 05:25:28 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+2 \cot \left (x \right ) y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 12

dsolve(diff(y(x),x$2)+2*cot(x)*diff(y(x),x)-y(x)=0,y(x), singsol=all)
 

\[ y = \csc \left (x \right ) \left (c_{2} x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 15

DSolve[D[y[x],{x,2}]+2*Cot[x]*D[y[x],x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (c_2 x+c_1) \csc (x) \]