47.4.4 problem 52

Internal problem ID [7481]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 2. Linear homogeneous equations. Section 2.2 problems. page 95
Problem number : 52
Date solved : Tuesday, January 28, 2025 at 03:10:46 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.934 (sec). Leaf size: 49

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

\[ y = \left (\cos \left (x \right )+1\right ) \operatorname {HeunC}\left (0, 1, -1, -2, \frac {3}{2}, \frac {\cos \left (x \right )}{2}+\frac {1}{2}\right ) \left (c_{1} +c_{2} \left (\int _{}^{\cos \left (x \right )}\frac {1}{\left (\textit {\_a} +1\right )^{2} \operatorname {HeunC}\left (0, 1, -1, -2, \frac {3}{2}, \frac {\textit {\_a}}{2}+\frac {1}{2}\right )^{2}}d \textit {\_a} \right )\right ) \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Not solved