I have the following exact equations, however, teacher said it is incorrect. Cannot find a mistake. Could you please help me?(adsbygoogle = window.adsbygoogle || []).push({});

(3x^2 - 2x - y) dx + (2y - x + 3y^2)dy = 0

This is exact equation, because:

P = (3x^2 - 2x - y)

Q = (2y - x + 3y^2)

P'y = Q'x = -1

Then integrate Intx P = x^3 - x^2 - yx + fi(y).

Find derivative: (x^3 - x^2 - yx + fi(y)'y = -x+ fi'(y) = Q = (2y - x + 3y^2).

Find fi'(y) = 2y + 3y^2. Iegūst fi(y) = y^3 + y^2.

Result: x^3 - x^2 - yx + y^3 + y^2 + C.

Where is a mistake? Mabybe the whole idea is incorrect? Please, help me.

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# Exact equations

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