dsolve(diff(diff(y(x),x),x) = -1/x/(x^2-1)*((1-4*a)*x^2-1)*diff(y(x),x)-((-v^2+x^2)*(x^2-1)^2+4*a*(a+1)*x^4-2*a*x^2*(x^2-1))/x^2/(x^2-1)^2*y(x),y(x))