find some constants $a$ and $b$ (not both zero), such that $u(x,y)=f(ax+by)$ is a generic solution, where $f$ is an arbitrary $C^1$ function.\

8a. $u_x+2u_y=0$\

Question

find some constants $a$ and $b$ (not both zero), such that $u(x,y)=f(ax+by)$ is a generic solution, where $f$ is an arbitrary $C^1$ function.\

8a. $u_x+2u_y=0$\

usukidoll · Answer

$$u_x+2u_y=0 $$

usukidoll · Answer

FInd some constants$$a$$ and $$b$$ not both zero such that $$u(x,y) = f(ax+by)$$ is a generic solution that satisfies the equation which is posted above. I want to know what the heck are they talking about?

hartnn · Answer

lol, even i am wondering what generic solution is and how to find it...

usukidoll · Answer

wait I'll give you the link to the book

usukidoll · Answer

http://books.google.com/books?id=tVXXD8sJ7uwC&pg=PA46&lpg=PA46&dq=generic+solution+pde&source=bl&ots=OkbSQ7cixK&sig=CQLtM7fYPSv3KA_UCpxzLEq7zy0&hl=en&sa=X&ei=8zEVVJPkAaOHjAKo44GgBg&ved=0CCwQ6AEwAQ#v=onepage&q=generic%20solution%20pde&f=false go down to page 46

usukidoll · Answer

I tried using example 5.... got me in a mess

usukidoll · Answer

@ganeshie8

usukidoll · Answer

any idea on how this works @hartnn?

hartnn · Answer

entirely new concept...

trying to find and use $u_x ,u_y$

hartnn · Answer

af' +2bf' =0

a+2b =0

usukidoll · Answer

the back of the book (the one I have a hardcopy) mentioned about a ratio a/b
a+2b = 0

like when a = 2 and b = -1  or something like that?!

hartnn · Answer

right, thats what i got 
just find u_x and u_y

hartnn · Answer

u = f(ax+by)

$u_x = f'(ax+by) (ax+by)' = af'(ax+by)$

similarly find u_y

usukidoll · Answer

wait how... and then what happens afterwards?

usukidoll · Answer

|dw:1410675821053:dw| like that?