Find d^2y/dx^2 in terms of x and y. 35. x^2 +xy =5?

Question

Problem is:
x^2 +xy =5

Answer 1

dy/dx:
2x + (xdy + y) = 0

d2y/dx2:
2 + xd2y + dy + dy = 0
2 + xd2y + 2dy = 0
xd2y = -2 - 2dy
d2y = (-2 - 2dy)/x

d2y is the same as d2y/dx2 - I just used d2y since it's assumed that we're taking derivatives with respect to x, and it's easier to type.