In Exercises 22-25, the equations are not exact. However, if you multiply by the given integrating factor, then you can solve the resulting exact equation. 22. $(y^2 - xy)dx + x^2dy = 0$, $\mu(x, y) = \frac{1}{xy^2}$ 23. $(x^2y^2 - 1)y dx + (1 + x^2y^2)x dy = 0$, $\mu(x, y) = \frac{1}{xy}$
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To check if it is exact, we calculate the partial derivatives: ∂M/∂y = 1 ∂N/∂x = 1 Since ∂M/∂y is not equal to ∂N/∂x, the equation is not exact. To make it exact, we need to find an integrating factor. The integrating factor is given by: μ(x) = e^(∫(∂N/∂x - Show more…
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