Internal problem ID [7505]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 788.
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 }-2 x y^{\prime }+30 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 73
dsolve((1-x^2)*diff(y(x),x$2)-2*x*diff(y(x),x)+30*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (\frac {21}{5} x^{5}-\frac {14}{3} x^{3}+x \right )+c_{2} \left (\frac {\left (945 x^{5}-1050 x^{3}+225 x \right ) \ln \left (x -1\right )}{28800}+\frac {\left (-945 x^{5}+1050 x^{3}-225 x \right ) \ln \left (x +1\right )}{28800}+\frac {21 x^{4}}{320}-\frac {49 x^{2}}{960}+\frac {1}{225}\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 66
DSolve[(1-x^2)*y''[x]-2*x*y'[x]+30*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{8} x \left (7 c_2 x \left (7-9 x^2\right )+c_1 \left (63 x^4-70 x^2+15\right )\right )+\frac {1}{8} c_2 x \left (63 x^4-70 x^2+15\right ) \tanh ^{-1}(x)-\frac {8 c_2}{15} \\ \end{align*}