Internal problem ID [7473]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 754.
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 }+12 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 53
dsolve((1-x^2)*diff(y(x),x$2)-2*x*diff(y(x),x)+12*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (-\frac {5}{3} x^{3}+x \right )+c_{2} \left (\frac {\left (15 x^{3}-9 x \right ) \ln \left (x -1\right )}{72}+\frac {\left (-15 x^{3}+9 x \right ) \ln \left (x +1\right )}{72}+\frac {5 x^{2}}{12}-\frac {1}{9}\right ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 44
DSolve[(1-x^2)*y''[x]-2*x*y'[x]+12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} \left (3 c_1 x \left (5 x^2-3\right )+c_2 \left (-15 x^2+3 \left (5 x^2-3\right ) x \tanh ^{-1}(x)+4\right )\right ) \\ \end{align*}