Question

Classify the differential equation as separable, linear, or exact, and solve by one of these methods. It is possible to have more than one classification. Express your answer in the form F(x, y) = C (in other words, an equation set = to a constant). note: you must verify exactness by showing a test when solving exact equations. (yeˣʸ+2x)dx +(xeˣʸ - 2y)dy = 0

Answer 1

The given differential equation is not separable, linear, or exact.

Step-by-step explanation:

The given differential equation is:

(yex*y+2x)dx +(xex*y - 2y)dy = 0

To classify the equation, we need to check if it is separable, linear, or exact.

By observing the equation, we can see that it is not separable since the variables 'x' and 'y' are not separated.

It is also not linear as it contains the terms 'xy' and 'yexy'.

To check for exactness, we can find the partial derivatives of the coefficients:

∂M/∂y = 2exy - 2

∂N/∂x = exy - 2exyy

Since ∂M/∂y is not equal to ∂N/∂x, the equation is not exact.

Therefore, the given differential equation is neither separable, linear nor exact.