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Show that the differential equation x(dy...

Show that the differential equation `x(dy)/(dx)=y-x tan(y/x)` is homogenous and solve it.

Text Solution

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The given differential equation may be written as
`(dy)/(dx)=y/x-tany/x`…………….(i)
This is of the form, `(dy)/(dx)=f(y/x)`.
So,the given differential equation is homogeneous.
Putting, `y=vx` and `(dy)/(dx)=v+x(dv)/(dx)` in (i), we get
`v+x(dv)/(dx)=v-tanv`
`rArr x(dv)/(dx)=-tanv`
`rArr (dv)/(tanv)=-(dx)/x`
`rArr
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