Question

1. Sove
Sone (-2xy-g² ) dx - (x + y 3 dy=0)​

Answer 1

Answer:

3x2y3 − 5x4) dx + (y + 3x3y2) dy = 0

In this case we have:

M(x, y) = 3x2y3 − 5x4

N(x, y) = y + 3x3y2

We evaluate the partial derivatives to check for exactness.

∂M∂y = 9x2y2

∂N∂x = 9x2y2

They are the same! So our equation is exact.

We can proceed.

Now we want to discover I(x, y)

Let's do the integration with x as an independent variable:

I(x, y) = ∫M(x, y) dx

= ∫(3x2y3 − 5x4) dx

= x3y3 − x5 + f(y)

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