Internal problem ID [6543]
Book: Own collection of miscellaneous problems
Section: section 5.0
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 \cot \relax (x ) y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(diff(y(x),x$2)+2*cot(x)*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{\sin \relax (x )}+\frac {c_{2} x}{\sin \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 15
DSolve[y''[x]+2*Cot[x]*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (c_2 x+c_1) \csc (x) \\ \end{align*}