Could anyone check my work as attached?
pdf 250 part ii. Find the explicit general solution
pdf 252. Find the particular solution for the given IC.
A couple of comments. For your first PDE, you have a 1/2 missing. But on a note, you want to solve the characteristic equations
Which you pick pairs. You chose
Why would you not choose the second pair as
? It so much easier and the y is not needed.
For your second PDE you have in one of your lines
Where did this come from?
. rearranging for u I get
which i believe is the same as attachment when the missing 1/2 is factored in.
, this satisfies the original DE and IC's