solve differential equation sqrt 1+x2+y2+x2y2 + xy dy/dx=0

(1 + x2)(1 + y2) + xydy/dx = 0

(1/x + x)dx = -ydy/(1+y2)

integrating we get

ln x + x2/2  + C= - ln(1 + y2)

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There's square root in the expresiion.!!

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 i am sorry i didnot see the sqrt

ok the solution then is 

√(1+x2)/x = ydy/√(1+y2)

integrating the above eqn we get

put 1 + x2 =t and dx = dt/2x ie 

tdt / 2(t2-1) = 2√(1+y2)

ln(t2 -1) / 2 + C = 2√(1+y) 

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i guess u missed -ve sign when taking
xydy/dx on the other side
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sqrt(1+x2)dx/x = sqrt(1+x2) - arctanh(sqrt(1+x2))

https://www.symbolab.com

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here it is

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