Internal problem ID [7458]
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)]`]]
\[ \boxed {\left (1-x^{2}\right ) y^{\prime \prime }-x y^{\prime }-c^{2} y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve((1-x^2)*diff(y(x),x$2)-x*diff(y(x),x)-c^2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (x +\sqrt {x^{2}-1}\right )^{i c}+c_{2} \left (x +\sqrt {x^{2}-1}\right )^{-i c} \]
✓ Solution by Mathematica
Time used: 0.09 (sec). Leaf size: 89
DSolve[(1-x^2)*y''[x]-x*y'[x]-c^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \cos \left (\frac {1}{2} c \left (\log \left (1-\frac {x}{\sqrt {x^2-1}}\right )-\log \left (\frac {x}{\sqrt {x^2-1}}+1\right )\right )\right )-c_2 \sin \left (\frac {1}{2} c \left (\log \left (1-\frac {x}{\sqrt {x^2-1}}\right )-\log \left (\frac {x}{\sqrt {x^2-1}}+1\right )\right )\right ) \]