1st order differential equation

[Firepanda]

It says find any solution y(x) of

xy' = 1 + y^2

I rearranged into seperable form to get

dy/(1+y^2) = dx/x

Integrated both sides to get

arctan y = lnx + C

then y(x) = tan(lnx + C)

Is this ok? I'm a little struck on find 'any' solution for this, not too sure how else I could have done it.

Perhaps I didn't do it correct?

 

[Dick]

I think you found all the solutions. If you want to find ANY specific solution then just set C=any constant. I'm not sure why you think you did something wrong.