Internal problem ID [6789]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 57.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Gegenbauer]
Solve \begin {gather*} \boxed {\left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }-4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.129 (sec). Leaf size: 45
dsolve((1-x^2)*diff(y(x),x$2)-5*x*diff(y(x),x)-4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x}{\left (x^{2}-1\right )^{\frac {3}{2}}}+\frac {c_{2} \left (-\ln \left (x +\sqrt {x^{2}-1}\right ) x +\sqrt {x^{2}-1}\right )}{\left (x^{2}-1\right )^{\frac {3}{2}}} \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 49
DSolve[(1-x^2)*y''[x]-5*x*y'[x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-c_2 \sqrt {x^2-1}+c_2 x \tanh ^{-1}\left (\frac {x}{\sqrt {x^2-1}}\right )+c_1 x}{\left (x^2-1\right )^{3/2}} \\ \end{align*}