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For a partial differential equation, in a function φ (x, y) and two variables x, y, what is the form obtained after separation of variables is applied?

For a partial differential equation, in a function φ (x, y) and two variables x, y, what is the form obtained after separation of variables is applied? Correct Answer Φ (x, y) = X(x)Y(y)

The method of separation of variables relies upon the assumption that a function of the form, Φ (x, y) = X(x)Y(y) will be a solution to a linear homogeneous partial differential equation in x and y. This is called a product solution and provided the boundary conditions are also linear and homogeneous this will also satisfy the boundary conditions.

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