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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:`x y = log y + C` : `yprime=(y^2)/(1-x y)(x y!=1)`

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`xy=logy+C`
differentiate w.r.t.x
`x*(dy)/(dx)+y*1=(1)/(y)*(dy)/(dx)+0`
`implies (1)/(y)(dy)/(dx)-x(dy)/(dx)=y`
`implies ((1)/(y)-x)(dy)/(dx)=y`
`implies (1-xy)(dy)/(dx)=y^(2)`
`implies (dy)/(dx)=(y^(2))/(1-xy)`
`implies y'=(y^(2))/(1-xy)(xy ne 1)`
Therefore, `xy=logy+c` is the solution of given differential equation.
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