DSolve[Derivative[2][y][x] == -(((4*a*(1 + a)*x^4 - 2*a*x^2*(-1 + x^2) + (-1 + x^2)^2*(-v^2 + x^2))*y[x])/(x^2*(-1 + x^2)^2)) - ((-1 + (1 - 4*a)*x^2)*Derivative[1][y][x])/(x*(-1 + x^2)),y[x],x]