Find the general solution of the differential equation `(dy)/(dx) = (y)/(x) + cos.(y)/(x)`.

Explanation

`(dy)/(dx) = (y)/(x) + cos.(y)/(x)`
Putting y = vx
`rArr (dy)/(dx) = v + x(dv)/(dx)`
We get,
`v + x(dv)/(dx) = v+ cos v`
`rArr sec v dv = (dx)/(x)`
Integrating both sides, we get
`int sec v dv = int (dx)/(x)`
`rArr ln|(sec v + tan v)| = ln|x| + ln c`
`rArr |(sec.(y)/(x) + tan.(y)/(x))| = c|x|`