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The equation $f_W = \sigma f$ is treated as an ordinary differential equation because it involves differentiation only with respect to $W$, and the variable $t$ does not appear in the derivative structure, acting merely as a parameter.

Conditions: $\sigma$ is a constant.; The equation is considered with respect to $W$ while $t$ is held fixed.

The equation $f_W = \sigma f$ is treated as an ordinary differential equation because it involves differentiation only with respect to $W$, and the variable $t$ does not appear in the derivative structure, acting merely as a parameter.

Conditions: $\sigma$ is a constant.; The equation is considered with respect to $W$ while $t$ is held fixed.