Internal problem ID [7383]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 664.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Gegenbauer]
Solve \begin {gather*} \boxed {\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.116 (sec). Leaf size: 57
dsolve((1-4*x^2)*diff(y(x),x$2)-20*x*diff(y(x),x)-16*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x}{\left (4 x^{2}-1\right )^{\frac {3}{2}}}+\frac {c_{2} \left (2 \ln \left (2 x +\sqrt {4 x^{2}-1}\right ) x -\sqrt {4 x^{2}-1}\right )}{\left (4 x^{2}-1\right )^{\frac {3}{2}}} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 57
DSolve[(1-4*x^2)*y''[x]-20*x*y'[x]-16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-2 c_2 x \operatorname {ArcSin}(2 x)-c_2 \sqrt {1-4 x^2}+c_1 x}{\sqrt [4]{1-4 x^2} \left (4 x^2-1\right )^{5/4}} \\ \end{align*}