Question

Determine whether the equation is exact. If it is, then solve it. eᵗ (9y−5t)dt+(8+9eᵗ )dy=0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The equation is exact and an implicit solution in the form F(t,y)=C is =C, where C is an arbitrary constant. (Type an expression using t and y as the variables.)
B. The equation is not exact.

Answer 1

The given equation is not exact, so it cannot be solved using the method of finding an integrating factor.

Step-by-step explanation:

The given equation is:

`eᵗ (9y−5t)dt+(8+9eᵗ )dy=0`

To determine if it is exact, we need to check if the partial derivatives of the coefficient functions are equal. Let's find the partial derivatives:

`∂/∂y (9y−5t) = 9∂/∂t (8+9eᵗ ) = 9eᵗ\\`

The derivatives are not equal, so the equation is not exact. We cannot solve it using the method of finding an integrating factor.

Therefore, the correct choice is B. The equation is not exact.