Let u(x, y, t) = (1/t)exp[-(x^2 + y^2)/4t], where exp denotes e to the power of a function. Show that u(x, y, t) satisfies the 2-dimensional heat equation ut = uxx + uyy. Hint: product rule...
Added by Ellen R.
Step 1
ut = d/dt[(1/t)exp[-(x^2 + y^2)/4t]] = -1/t^2 * exp[-(x^2 + y^2)/4t] + (1/t) * (1/4t^2) * (x^2 + y^2) * exp[-(x^2 + y^2)/4t] = -1/t^2 * exp[-(x^2 + y^2)/4t] + (x^2 + y^2)/(4t^3) * exp[-(x^2 + y^2)/4t] ** Show more…
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