Internal problem ID [6702]
Book: Second order enumerated odes
Section: section 2
Problem number: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Gegenbauer, [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }-c^{2} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 39
dsolve((1-x^2)*diff(y(x),x$2)-x*diff(y(x),x)-c^2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (x +\sqrt {x^{2}-1}\right )^{i c}+c_{2} \left (x +\sqrt {x^{2}-1}\right )^{-i c} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 42
DSolve[(1-x^2)*y''[x]-x*y'[x]-c^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cos \left (c \tanh ^{-1}\left (\frac {x}{\sqrt {x^2-1}}\right )\right )+c_2 \sin \left (c \tanh ^{-1}\left (\frac {x}{\sqrt {x^2-1}}\right )\right ) \\ \end{align*}