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Verify that the given functions (explic...

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:`y -cos y = x` : `(y sin y + cos y + x) y' = y`

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`y-cosy=x`……..`(1)`
differentiating we get,
`(dy)/(dx)+siny*(dy)/(dx)=1`
`implies (dy)/(dx)=(1)/(1+siny)`
Now, `L.H.S=(y sin y+cosy+x)(dy)/(dx)`
`=(y sin y+cosy+y-cosy)*(1)/(1+siny)` [from equation `(1)`]
`=(y sin y+y)(1)/(1+siny)`
`=y=R.H.S`
Therefore, `y-cosy=x` is the solution of given differential equation.
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