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homogeneous PDE

A linear PDE whose every term contains the unknown function or one of its derivatives -- no term depends only on the independent variables.

A linear PDE $L[u] = g(x)$ is homogeneous when $g\equiv0$ , so that $u\equiv0$ is always a solution and every solution is built from the differential operator $L$ acting on $u$ alone.

See also

inhomogeneous PDE linear PDE

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