# <span lang="EN-US

Given that

Differentiating with respect to itself, we get

Simplifying, we get

x dx + y dy = x dy – y dx

or

dx(x + y)= dy(x-y)

Hence,

OR

Given that xy-yx=ab

Let u= xy and v= yx, then we get

u-v= ab

Differentiating with respect to x, we get

(Since ab is constant) …. (1)

u= xy

Taking log both sides

Differentiating with respect to x, we get

Hence, ….. (2)

v= yx

Taking log both sides

Differentiating with respect to x, we get

Hence, ……(3)

Substituting (2) and (3) in (1), we get

Simplifying, we get

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