If g is an arbitrary differentiable function of one variable, then

is a solution of

Attempt:

How am I suppose to show this:

Thanks.

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- Dec 25th 2010, 03:25 PMdwsmithu(x,y) is a solution to 3u_x+4u_y-2u=1
If g is an arbitrary differentiable function of one variable, then

is a solution of

Attempt:

How am I suppose to show this:

Thanks. - Dec 25th 2010, 04:02 PMzzzoak
Let

There is a mistake. The chain rule

Also

- Dec 25th 2010, 04:04 PMdwsmith
- Dec 25th 2010, 04:28 PMzzzoak
For example consider the function

and find

- Dec 25th 2010, 04:31 PMdwsmith
I believe you. I was just asking.

I edited the original post. How can I show g_y=g_x because that is the only way it will be 0? - Dec 25th 2010, 04:37 PMzzzoak
Please look post #2.

Instead of

there must be

- Dec 25th 2010, 04:48 PMdwsmith

- Dec 25th 2010, 05:06 PMzzzoak