Determine whether the given function satisfies a Laplace equation. f(x, y) = e^(3y) sin 3x Yes or No?
Added by Kristina G.
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In two dimensions, this becomes: ∂²f/∂x² + ∂²f/∂y² = 0 Taking the partial derivatives of f(x,y), we get: ∂f/∂x = 3e^(3y)cos(3x) ∂²f/∂x² = -9e^(3y)sin(3x) ∂f/∂y = 3e^(3y)sin(3x) ∂²f/∂y² = 9e^(3y)sin(3x) Plugging these into the Laplace equation, we Show more…
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