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Express the following differential equat...

Express the following differential equations in the form `(dy)/(dx) = F((y)/(x))`.
(i) `xdy - ydx = sqrt(x^(2) + y^(2))dx`
(ii) `[x - y Tan^(-1)((y)/(x))] dx + x Tan^(-1)((y)/(x)) dy = 0`
(iii) `xdy = y(log y - log x+1)dx`

Text Solution

Verified by Experts

The correct Answer is:
(i) `(dy)/(dx) = (y)/(x) + sqrt((1+((y)/(x))^(2)))`
`(dy)/(dx) = ((y)/(x) Tan^(-1)((y)/(x))-1)/(Tan^(-1)((y)/(x)))`
(iii) `(dy)/(dx) = (y)/(x)[log((y)/(x))+1]`
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