On a system of PDE Let f 1 </msub> ( p 1 </msub> ,

rjawbreakerca

rjawbreakerca

Answered question

2022-07-09

On a system of PDE
Let f 1 ( p 1 , p 2 ) and f 2 ( p 1 , p 2 ) be two functions. The system of equations on R 2 is just:
p 1 p 1 f 1 + p 2 p 1 f 2 = 0
p 1 p 2 f 1 + p 2 p 2 f 2 = 0
So nobody complain, I want the solutions to be at least of class C 2 .

Answer & Explanation

Oliver Shepherd

Oliver Shepherd

Beginner2022-07-10Added 24 answers

( p 2 e q 1 ) p 1 p 1 , p 2 f 1 + p 2 p 1 , p 2 f 2 = p 1 f 2
So
(*) p 1 f 2 = p 2 f 1
Can you take from here? Now you have PDEs in one unknown. Solve and check whether their solution satisfies (*)...
Addison Trujillo

Addison Trujillo

Beginner2022-07-11Added 6 answers

I have been looking for an answer to this question for a very long time, thank you very much!

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