GATE EC 2022 Set 1 — Question 25

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MSQ+1 / -0MediumPDE by Separation of VariablesDifferential EquationsEngineering Mathematics

Engineering Mathematics → Differential Equations → PDE by Separation of Variables

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Question

Consider the following partial differential equation (PDE)a2f(x,y)x2+b2f(x,y)y2=f(x,y),a \frac{\partial^2 f(x, y)}{\partial x^2} + b \frac{\partial^2 f(x, y)}{\partial y^2} = f(x, y),where aa and bb are distinct positive real numbers. Select the combination(s) of values of the real parameters ξ\xi and η\eta such that f(x,y)=e(ξx+ηy)f(x, y) = e^{(\xi x + \eta y)} is a solution of the given PDE.
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