Internal problem ID [5060]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\cot \relax (x ) y^{\prime }+\cos \relax (x ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 2.844 (sec). Leaf size: 65
dsolve(diff(y(x),x$2)-cot(x)*diff(y(x),x)+cos(x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (1+\cos \relax (x )\right ) \HeunC \left (0, 1, -1, -2, \frac {3}{2}, \frac {\cos \relax (x )}{2}+\frac {1}{2}\right )+c_{2} \left (1+\cos \relax (x )\right ) \HeunC \left (0, 1, -1, -2, \frac {3}{2}, \frac {\cos \relax (x )}{2}+\frac {1}{2}\right ) \left (\int _{}^{\cos \relax (x )}\frac {1}{\left (\textit {\_a} +1\right )^{2} \HeunC \left (0, 1, -1, -2, \frac {3}{2}, \frac {\textit {\_a}}{2}+\frac {1}{2}\right )^{2}}d \textit {\_a} \right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y''[x]-Cot[x]*y'[x]+Cos[x]*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved