Partial derivative equation problem

AI Thread Summary
The discussion centers on a user struggling to solve a partial differential equation and seeking help with the solution provided in a PDF. Initial confusion about the equation's nature leads to a misunderstanding, as the user mistakenly identifies it as non-linear. Other participants clarify that it is a linear partial differential equation and encourage the user to apply their knowledge of partial derivatives. The user expresses intent to try different methods to solve the equation, indicating a willingness to seek further assistance if needed. Overall, the conversation emphasizes the importance of understanding the equation's classification and applying relevant mathematical concepts.
RenOdur
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well i have been trying to solve this equation and i just can't...
the solution is given and it's at the second pdf file but i can't understand the procedure can somebody please help?
 

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Have you done any calculations at all yet as an attempt? What do you think you should do? :smile:

Hint: Think about what you know about partial derivatives, and also how you could get those equations into the forms required to help obtain the answers. :wink:
 
well i initially thought about integration...but really i have no clue about it since i haven't be teached yet how to solve nonlinear differential equations(at least that's what I think this equation is,correct me if I'm wrong)
 
No, that is not a non-linear partial differential equation. Why would you think it is non-linear?
 
ok so it's a linear partial differential equation...i'll try some ways out and if I still can't solve it i'll let you know:)
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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