Folks,
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.
Thanks
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
and
.
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?
I guess I overlooked this simpler option. If we use this option, I calculate
. rearranging for u I get
which i believe is the same as attachment when the missing 1/2 is factored in.
Ok, I believe I have it. Silly mistakes as usual. It should just be under the square root and I also forgot a constant of integration which would be a function of k. Hence I get the particular solution to be
, this satisfies the original DE and IC's
Thanks Danny!