I face with a quasi-solvable ode
$x^{2}(1+x^{2})y''+2xy'+A(1+x^{2})^{2}y=0$
where $A$ is a constant. I am trying to find a solution for this ode. My suggestion is that we can rewrite the above equation as
$x^{2}(1+x^{2})y''+2xy'+A(1+2x^{2})y=-Ax^{4}y$
Then, the left side is a hypergeo polynomial. But i have no idea about the right side. How can i find the complete solution of this ode?