(a) Can every first order ODE be written in the form N(x, y) + M(x, y)y' = 0? Explain or give a counterexample. When is a unique solution guaranteed? (b) Suppose there exists an integrating factor u = p(x, y) such that AN(x, y) +AM(x, y)y' = 0 is exact. Write a differential equation in terms of . Describe this equation as lin- earonlinear, homogeneouson-homogeneous, or use any other descriptions that apply. (c) Suppose z is a differentiable funtion such that z : R2 - R, z = z(x, y). Suppose also that u = (u* oz)(x, y), where * is also differentiable. Simplify the equation in part (b) and find * Why is it now possible to find an integrating factor using techniques from this class? (d) Continue your work in part (c) and find a formula for / as well as a necessary and sufficient condition for this integrating factor. (e) Give an example of an equation that can be solved using the integrating factor in (d). Solve this equation