(10 points) Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(x, y)F(x, y) whose level curves are solutions to the differential equation (−2exsin(y)−3y)dx+(−5x+excos(y))dy= 0

The equation is not exact.

Step-by-step explanation:

Given the differential equation:

(-2e^x sin(y) - 3y)dx - (-5x + e^x cos(y))dy = 0

We need this equation to be in the form:

Mdx + Ndy = 0

Where M = M(x, y) and N = N(x, y)

to verify its exactness.

So, rewriting the equation, we have

(-2e^x sin(y) - 3y)dx + (5x - e^x cos(y))dy = 0

Now, if ∂N/∂x = ∂M/∂y, the equation is exact.

Here, M(x, y) = (-2e^x sin(y) - 3y), and N(x, y) = (5x - e^x cos(y))

(∂/∂x)(-2e^x sin(y) - 3y) = -2e^x sin(y)

(∂/∂y)(5x - e^x cos(y)) = e^x sin(y)

Since ∂N/∂x ≠ ∂M/∂y, we say the equation is not exact, and hence, we are not required to find its general solution.

you never say the total so we cant find the percentage used for petrol

step-by-step explanation: