Internal problem ID [8941]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1362.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (x^{2}-1\right ) y^{\prime \prime }-2 x^{3} y^{\prime }-\left (\left (a -n \right ) \left (a +n +1\right ) x^{2} \left (x^{2}-1\right )+2 a \,x^{2}+n \left (n +1\right ) \left (x^{2}-1\right )\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.594 (sec). Leaf size: 109
dsolve(x^2*(x^2-1)*diff(diff(y(x),x),x)-2*x^3*diff(y(x),x)-((a-n)*(a+n+1)*x^2*(x^2-1)+2*a*x^2+n*(n+1)*(x^2-1))*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \HeunC \left (0, -n -\frac {1}{2}, -2, -\frac {1}{4} a^{2}+\frac {1}{4} n^{2}-\frac {1}{4} a +\frac {1}{4} n , -\frac {1}{4} n^{2}-\frac {1}{4} n +\frac {3}{4}+\frac {1}{4} a^{2}-\frac {1}{4} a , x^{2}\right ) x^{-n}+c_{2} \HeunC \left (0, n +\frac {1}{2}, -2, -\frac {1}{4} a^{2}+\frac {1}{4} n^{2}-\frac {1}{4} a +\frac {1}{4} n , -\frac {1}{4} n^{2}-\frac {1}{4} n +\frac {3}{4}+\frac {1}{4} a^{2}-\frac {1}{4} a , x^{2}\right ) x^{n +1} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y''[x] == -(((2*a*x^2 + n*(1 + n)*(-1 + x^2) + (a - n)*(1 + a + n)*x^2*(-1 + x^2))*y[x])/(x^2*(-1 + x^2))) + (2*x*y'[x])/(-1 + x^2),y[x],x,IncludeSingularSolutions -> True]
Not solved