Determine whether or not the following equation is exact if

Question

1. Determine whether or not the following equation is exact. If it is exact, find the solution.

(e^xsin y - 5y sin x)dx + (e^x cos y + 5 cosx)dy = 0.

2. Determine whether or not the following equation is exact. If it is exact, find the solution.

(7y + (1/x) - (x/y²)) dy/dx + (2x + (1/y) - (y/x²)) = 0.

3. Determine whether or not the following equation is exact:

2e^(x/2)+y - y + 2 (xe^(x/2)+y +1) (dy/dx) = 0. y(0)=1

If it is exact, find the solution. If it is not exact, multiplying the equation with an integrating factor F=e^-x/2 and check if the new equation is exact. If the new equation is exact, find the solution.