For the diff eq. (dy/dx)=(1-y)/x, I see that it is not continuous or defined at x=0. however, if you graph the solution y=cx+1, then you get solutions passing thru (0,1). This violates the existence part of the existence and uniqueness theorem doesn't it? I mean, I see that uniqueness fails because the partial derivative with respect to y of f is not defined at x=0. But the existence part should fail everywhere on x=0 as well. But it does not at 0,1. Many solution curves pass through there. ? Please help.

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