Math 3363 Fall 2015 Homework 3 Due November 10 Please use a pencil and do the problems in the order in which they are listed. Write on only one side of each page and staple your pages. 1. Suppose that each of , , and is a positive number. Derive the solution to 2 2 2 ( ) + 2 ( ) + 2 ( ) 2 for 0 ( 0) ( ) for 0 (0 ) ( ) ( 0 ) ( ) = 0 = = = = = = (1) 0 and 0 0 for 0 and 0 (2) ( ) (3) and 0 0 for 0 and 0 (4) 0 for 0 and 0 (5) 0 for 0 and 0 (6) 0 for 0 and 0 (7) Begin by looking for solutions of the form ( ) = ( )() 2. Find the equilibrium solution for ( ) (0 ) (1 ) ( 0) 2 ( ) + for 0 1 and 0 2 = 0 for 0 = (1) (2) = 0 for 0 and (3) = () for 0 1 (4) 3. Find the solution to ( ) (0 ) (1 ) ( 0) 2 ( ) + for 0 1 and 0 2 = 0 for 0 = (1) (2) = 0 for 0 and (3) = 0 for 0 1 (4) 1 Begin by letting ( ) = ( ) () where is the equilibrium solution found in Problem 2. State and solve the corresponding problem for . Give the solution 4. Find the solution to ( ) (0 ) (1 ) ( 0) 2 ( ) + for 0 1 and 0 2 = 0 for 0 = (1) (2) = 0 for 0 and (3) = 1 for 0 1 (4) Use the method given in item 8.5 in your notes. 2