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

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

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(dy)/(dx)=x+xy

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

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

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

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

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

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

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

(dy)/(dx)=xy+2y+x+2

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