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