1.

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

Answer»


Answer :(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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