INSTRUCTIONS: Consider the differential equation

1. ysecxdx+sinxdy=0.

Do the following:

-Verify that this equation is not an exact differential equation

-Verify that sec x is an integrating factor (That is, multiple the given equation with the integrating factor and verify that the resulting equation is an exact equation)

-Solve the exact equation using the of solving exact equations. Show as much detail on your solving as you can. Your general solution must be y tan x = C

2. (exsiny)dx+(cosy)dy=0 Do the following:

-Verify that this equation is not an exact differential equation

-Solve the integrating factor of the equation using Case 1.

-Verify that the resulting equation with the integrating factor is an exact equation.

3. xydx+(1+x2)dy=0

Do the following:

-Verify that this equation is not an exact differential equation

-Solve the integrating factor of the equation using Case 2.

-Verify that the resulting equation with the integrating factor is an exact equation.