PDE-Lagrange's Method (Choosing multiplier such that denominator becomes zero)

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Good Afternoon. you may post your questions on Lagrange's method here or send it directly to me

appliedmathematics
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Mam is there any rule for choosing multiplier that it should be always linear

DTMASUYASHMISHRA
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is there any method to get those multipliers

solomonmonday
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Is there any tricks to identify multipliers

Akash-vsyh
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ma'am how is the multiplier equation equal to the auxiliary equation?

vik_
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mam integration karne ke baad denominatior ka 2 kese nikala

robinroy
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(ly-mz)p + (mz-nx)q = (nx-ly) Please anyone tell what multiplier should we use in both cases, (In 1 Case it will be 1, 1, 1) but in other what it would be?
There are several video solution on a bit different question, but i am not getting solution for this Question.

Chauhan_Amit
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Ma'am how did u choose the multipliers as x, -y, -z and y, x, -z

deepakgoud