Question

How to tell whether a differential is exact vs inexact?

Answer 1

this is the differential I am given:

df = (2xy - 9x^2)dy + (2y+x^2+1)dx

@Nnesha @sillybilly123 @hero

Answer 2

you would typically rely on the fact that the mixed partial is the same, whichever way calculated. ie \(f_{xy} = f_{yx}\)

so if \(f = f(x,y) \color{red}{= const}\), then \(df = f_x dx + f_y dy = 0\)

if your case:

- \(f_y = 2xy - 9x^2 \implies f_{yx} = 2y\)

- \(f_x = 2y+x^2+1 \implies f_{xy} = 2\)

not the same