Question

implicit differentiation
y-x=y(x+y)
find y''

Answer 1

y' - 1 = y'(x+y)+(1+y')(y)
y'-1 = xy'+yy' +y+yy'
y' -xy'-yy'-yy' = y+1
y'(1-x-2y) = y+1
solve for y'
should be
\[y' =\frac{ y+1 }{ 1-x-2y }\]

Answer 2

how about y''?

Answer 3

take d/dx of y'

Answer 4

\[y" =\frac{ y'(1-x-2y)-(y+1)(-1-2y') }{(1-x-2y)^2 }\]
wherever you see a y' plug equation u got for y'
it's a really messy problem...