Question


(a) Show that a function u(x,y)=e^(x^2-y^2 ) sin⁡(2xy) satisfies two dimensional Laplace equation

(∂^2 u)/(∂x^2 )+(∂^2 u)/(∂y^2 )=0

(b) Show that mixed second order partial derivatives of f(x,y)=2xe^y-3ye^(-x) are equal.

 

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Multivariable Calculus

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