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Laplace's equation has no source term, meaning it is homogeneous. Poisson's equation has a source term, meaning that the Laplacian applied to a scalar valued function is not necessarily zero. Poisson's equation is essentially a general form of Laplace's equation
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⭐ Laplace's equation has no source term, meaning it is homogeneous. Poisson's equation has a source term, meaning that the Laplacian applied to a scholar valued function is not necessarily zero. Poisson's equation is essentially a general form of Laplace's equation. ⭐
Its like the old saying from geometry goes : "All squares are rectangle but not all rectangles are square." In this setting, we can say, "All instances of Laplace's equation are also instances of Poisson's equation, but not all instances of Poisson's equation are instances of Laplace's equation.