First we must separate the variables:

`(2\ dy)/y=((x+1)dx)/x`

This gives us: `(2\ dy)/y=(1+1/x)dx`

We now integrate:

`int(2 dy)/y=int(1+1/x)dx`

`2 ln y=x+ln x+K`

Go back to Integration: Basic Logarithm Form if you are rusty on this integration.

We could continue with our solution and express `y` as an explicit function of `x`, as follows:

`ln y=(x+ln x+K)/2`

`y=e^((x+ln x+K)//2)`

Taking a typical constant value `K=1`, we have this solution graph:

1234-112345678910-1xyOpen image in a new page

Typical solution graph `y=e^((x+ln x+1)//2)`.

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