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## Main Question or Discussion Point

Hello!

From what I have read, a differential equation is exact if d^2f/dxdy = d^2f/dydx, is this correct? My professor has given us examples of dif. equations that are not exact. However I remember from last semester that Schwartz theorem states that the order in which you differentiate does not matter, the result is always the same. So d^2f/dxdy should always be equal to d^2f/dydx, so all diferential equations should be exact. This is obviously not right, but I don't understand why, can someone please explain?

Thank you!

From what I have read, a differential equation is exact if d^2f/dxdy = d^2f/dydx, is this correct? My professor has given us examples of dif. equations that are not exact. However I remember from last semester that Schwartz theorem states that the order in which you differentiate does not matter, the result is always the same. So d^2f/dxdy should always be equal to d^2f/dydx, so all diferential equations should be exact. This is obviously not right, but I don't understand why, can someone please explain?

Thank you!