### Homework due 1/21

### Section 1.1

2c-e, 3d-h, 4, 8, 11
### Section 1.2

2, 4, 5, 9
### Extra Problem on Section 1.2

Consider the two PDEs:

(a) y u_x - x u_y = 0

(b) y u_x - x u_y = f(x^2 + y^2)

1) Find the characteristic curve (x(t),y(t)) such that the PDE (a)
reduces to d/dt u(x(t),y(t)) = 0

2) Use the characteristic curve to solve (a) for u(x,y).

3) Now use the characteristic curve to solve (a) for u(x,y) subject
to the additional condition u(x,0) = x^2.

4) Use the characteristic curve to solve (b) for u(x,y). Are you
happy with your answer? If not, why not? How would you modify
the right-hand side so that you would be satisfied with your
solution? If the right hand side were f(x,y) then what is a
general condition that f(x,y) must satisfy?