Let D be a region in .

Let's denote: .

1. Prove that there is no non-trivial first order PDE

such as its set of soloution in D includes all the functions in K.

2. Find two non trivial differential equations of second order which are not equivalent and that all of the functions in K are soloutions for them both.

I'm pretty sure that in 1 we need to get some kind of a contradiction from fact that a function in K can be represented as:

...

Help is needed

Thanks