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

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

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

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

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

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

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

(1-x^(2))(dy)/(dx)-2xy=x-x^(3)

(1-x^(2))(dy)/(dx)-2xy=x-x^(3)

If log(sqrt(1+x^(2))-x)=ysqrt(1+x^(2)) , then show that (1+x^(2))(dy)/(dx)+xy+1=0 .

If y sqrt(x^(2)+1)= log (sqrt(x^(2)+1)-x) , prove that (x^(2)+1)(dy)/(dx) +xy+1=0 .