if 3x^2+5x+xy=1 y(1)=-7 and y'(1)= ?

Question

I can solve for dy/dx but I don't know what to do with y(1) and y'(1)

Answer 1

x y = -3 x^2 - 5 x + 1 ... y = - 3 x - 5 + 1/x ... so, y(1) = - 3 - 5 + 1 = -7

y' = dy/dx = - 3 - 1/x^2 ... so, y'(1) = - 3 - 1 = -4