What is the difference between simple fixed pole and simple movable

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The discussion clarifies the distinction between simple fixed poles and simple movable poles in differential equations. The equation z(dw/dz) + w = 0 has a simple fixed pole at z=0, independent of the integration constant c. In contrast, the equation (dw/dz) + w^2 = 0 features a simple movable pole at z=c, which is directly dependent on the value of c. This fundamental difference highlights the behavior of poles in relation to their constants in differential equations.

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What is the difference between simple fixed pole and simple movable pole?
Differential eqs. z(dw/dz)+w=0, corresponding solution w(z)=c/z, and (dw/dz)+w^2=0, corresponding solution w(z)=1/(z-c) where c being the integration constant. In the solution given above Ist equation has a simple fixed pole and IInd equation has a simple movable pole.
I don't see any difference between these solutions. Please clarify the above point clearly.

Thanks in well advance.
 
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Case w(z)=c/z : The pole is z=0 , not depending on c.
Case w(z)=1/(z-c) : The pole is z=c , so depending on c.
 

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