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

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

Solve the equation (1-x^(2))((dy)/(dx))+2xy=x sqrt(1-x^(2))

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

(dy)/(dx) + 2xy = x , given that y =1 when x =0

(dy)/(dx)=x+xy

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

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

Intergrating factor of the differential equaiton (x^(2)+1)(dy)/(dx)+2xy=x^(2)-1 is

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