Internal problem ID [8229]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 754.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Gegenbauer]
\[ \boxed {\left (1-x^{2}\right ) y^{\prime \prime }-2 x y^{\prime }+12 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 55
dsolve((1-x^2)*diff(y(x),x$2)-2*x*diff(y(x),x)+12*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (-\frac {5}{3} x^{3}+x \right )+c_{2} \left (-\frac {5 \ln \left (x +1\right ) x^{3}}{24}+\frac {5 \ln \left (x -1\right ) x^{3}}{24}+\frac {\ln \left (x +1\right ) x}{8}-\frac {\ln \left (x -1\right ) x}{8}+\frac {5 x^{2}}{12}-\frac {1}{9}\right ) \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 59
DSolve[(1-x^2)*y''[x]-2*x*y'[x]+12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} c_1 x \left (5 x^2-3\right )+c_2 \left (-\frac {5 x^2}{2}-\frac {1}{4} \left (5 x^2-3\right ) x (\log (1-x)-\log (x+1))+\frac {2}{3}\right ) \]