Find the general solution of the differential equation
`(x cos y) dy = e^(x) (x log x +1) dx.`

Explanation

The given differential equation may be written as
`cos y dy = (e^(x) log x +(e^(x))/(x))dx`
`rArr int cos y dy = int underset (I)((log x))underset(II)(e^(x)) dx+int (e^(x))/(x) dx +C, ` where C is an arbitrary constant
`rArr siny = (log x) e^(x) - int (1)/(x) *e^(x) dx + int (e^(x))/(x) dx + C`[integrating by parts]
`rArr sin y = (log x)e^(x) + C,` which is the required solution.