Please answer e,f,g

2. Consider M(,y) + N(x,y) = 0. (a) Suppose we can find a function F = F(1,y) so that F, = M and F, = N. Give an example of such an equation and solve it. # (b) Suppose we can find functions H and 2 so that (po 2)(I,y) is an integrating factor that transforms the given equation into an exact equation. What must be true about M and N? (c) Continuing from part (b), suppose we can find functions and 2 so that (102)(r, y) is an integrating factor that transforms the given equation into an exact equation. Construct a differential equation with respect to je to solve for f. (d) Using the ODE with respect to p in part (c), given (20) = po when does a unique solution exist? (e) Suppose 2 = 22 + y. Find from part (c), if possible. (f) Construct an example of an equation that can be solved using the integrating factor in part (e) and then solve this equation. (g) What sources did you use for this exercise? 2. Consider M(,y) + N(x,y) = 0. (a) Suppose we can find a function F = F(1,y) so that F, = M and F, = N. Give an example of such an equation and solve it. # (b) Suppose we can find functions H and 2 so that (po 2)(I,y) is an integrating factor that transforms the given equation into an exact equation. What must be true about M and N? (c) Continuing from part (b), suppose we can find functions and 2 so that (102)(r, y) is an integrating factor that transforms the given equation into an exact equation. Construct a differential equation with respect to je to solve for f. (d) Using the ODE with respect to p in part (c), given (20) = po when does a unique solution exist? (e) Suppose 2 = 22 + y. Find from part (c), if possible. (f) Construct an example of an equation that can be solved using the integrating factor in part (e) and then solve this equation. (g) What sources did you use for this exercise