Help to find compatible solution of PDEs

[khyrathussain123]

Dear members,

I need help to find compatible solution of following questions.

 

[DrPhil]

Dear members,

I need help to find compatible solution of following questions.

We need to see your work!

In particular, I have no idea what the notation means.

 

[khyrathussain123]

We need to see your work!

In particular, I have no idea what the notation means.

(1) Show that the PDEs xp = yq and z(xp – yq) = 2xy are compatible and hence find its solution.
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(2) Show that the PDEs [FONT=&quot][/FONT][FONT=&quot]p^2 + q^2 [/FONT][FONT=&quot][/FONT][FONT=&quot] = 1 and [/FONT][FONT=&quot][/FONT][FONT=&quot]( [/FONT]p^2 + q^2[FONT=&quot] [/FONT][FONT=&quot][/FONT][FONT=&quot])x = pz [/FONT]are compatible and hence find its solution.


​

 

[Deleted member 4993]

(1) Show that the PDEs xp = yq and z(xp – yq) = 2xy are compatible and hence find its solution.


(2) Show that the PDEs p^2 + q^2 = 1 and ( p^2 + q^2)x = pz are compatible and hence find its solution.


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Please share your work with us.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

We can help - we only help after you have shown your work - or ask a specific question (e.g. "are these correct?")

 

[stapel]

One of your equations is:

\(\displaystyle p^2\,+\,q^2\,=\,1\)

...but then you attach a thumbnail which contains, in part:

\(\displaystyle P\, =\, \frac{\partial z}{\partial x}\)

Are you, contrary to standard mathematical practice, intending \(\displaystyle P\) and \(\displaystyle p\) to indicate the same variable?

Thank you. :wink:

 

[khyrathussain123]

One of your equations is:

\(\displaystyle p^2\,+\,q^2\,=\,1\)

...but then you attach a thumbnail which contains, in part:

\(\displaystyle P\, =\, \frac{\partial z}{\partial x}\)

Are you, contrary to standard mathematical practice, intending \(\displaystyle P\) and \(\displaystyle p\) to indicate the same variable?

Thank you. :wink:

I have solve first question. but not able to solve second question.
Show that the PDEs p^2 + q^2 = 1 and ( p^2 + q^2)x = pz are compatible and hence find its solution.
where
\(\displaystyle p\, =\, \frac{\partial z}{\partial x}\)
\(\displaystyle q\, =\, \frac{\partial z}{\partial y}\)