Which of the following functions of u(x, y) is/are the solution of the equation: ?²u/?x² + ?²u/?y² = 0. A. None of these options. B. u(x, y) = x² + y² C. u(x, y) = x³ - 3xy² D. u(x, y) = x² - y² E. u(x, y) = e^x cos y
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Option A: $u(x,y) = e^{x+y}$ Let's check if this function satisfies the equation: $$\frac{\partial^2 u}{\partial x^2} = e^{x+y}$$ $$\frac{\partial^2 u}{\partial y^2} = e^{x+y}$$ Substituting these values in the given equation: $$\frac{\partial^2 u}{\partial Show more…
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