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(x^(2)-1)(dy)/(dx)+2xy=(2)/(x^(2)-1)...

(x^(2)-1)(dy)/(dx)+2xy=(2)/(x^(2)-1)

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(x^(2)+1)(dy)/(dx)=xy

(dy)/(dx) = (2xy)/(x^(2)-1-2y)

(dy)/(dx) = (2xy)/(x^(2)-1-2y)

(dy)/(dx) = (2xy)/(x^(2)-1-2y)

(1-x^(2))(dy)/(dx)-xy=1

(1-x^(2))(dy)/(dx)-xy=1

(1+x^(2))(dy)/(dx)+2xy=(1)/(1+x^(2));y=0 if x=1

The solution of differential equation (x^(2)-1) (dy)/(dx) + 2xy = 1/(x^(2)-1) is

(1-x^(2))(dy)/(dx)-xy=x^(2)