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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.2 Partial Derivatives, #37 · Multivariable Calculus · Partial derivatives

The equation for heat flow in the … plane is

The equation for heat flow in the $x y$ plane is $f_{t} = f_{xx} + f_{y y}$ . Show that $f (x, y, t) = e^{- 2 t} sin x sin y$ is a solution. What exponent in $f = e^{-___} sin 2 x sin 3 y$ gives a solution?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.2 Partial Derivatives, #37

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