Question

yzdx+zxdy+xydz=0 .what is the answer for this question
options are given above​

Answer 1

Answer:

b

Step-by-step explanation:

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Answer 2

SOLUTION

TO EVALUATE

$\displaystyle \sf{yz \: dx + zx \: dy + xy \: dz = 0 }$

EVALUATION

Here the given differential equation is

$\displaystyle \sf{yz \: dx + zx \: dy + xy \: dz = 0 }$

Dividing both sides by xyz we get

$\displaystyle \sf{ \frac{dx}{x} + \frac{dy}{y} + \frac{ dz}{z} = 0 }$

Integrating both sides we get

$\displaystyle \sf{ \int \frac{dx}{x} + \int \frac{dy}{y} + \int \frac{ dz}{z} = \ln\: c }$

$\displaystyle \sf{ \implies \: \ln x +\ln y + \ln z = \ln\: c }$

$\displaystyle \sf{ \implies \: \ln (xyz) = \ln\: c }$

$\displaystyle \sf{ \implies \: xyz =\: c }$

Where c is constant

FINAL ANSWER

Hence the required solution is

xyz = c

Where c is constant

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