1. (a) (8 points) Show that the differential equation 0

1. 2. 3. (a) (8 points) Show that the differential equation '2!J2 (l is not exact, but can be made exact using the integrating factor p(a:, y) y. Find the general solution (you may leave it in implicit form). (b) (2 points) Find thc solution of thc initial value problem for the DE of part (a) with initial condition y(l) = 3. (10 points) Find an integrating factor of the form p. for the differential equation Sin a: In 'Y + Y) + + In + Sin 'Y O and find the general solution (implicit form is 0K). (10 points) Find t,he general solution of -k y + h + 3m) y/ 0, y > 0.