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I'm new to Mathematica and have never solved a PDE before. I tried to follow a textbook to get equation 4, but got something different with Mathematica (I got $(4\pi Dt)^{1/2}$ instead of $(4\pi Dt)^{3/2}$). May I ask why I got the wrong answer and how can I fix that? Thank you so much!

Textbook:

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What I got:

enter image description here

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    $\begingroup$ Depends if the book is using $r \in \mathbb{R}$ or $r = (x, y, z) \in \mathbb{R}^{3}$. If it's the former then there is a typo in the book. If its the latter then the book is correct and you have not put the full set of coordinates into Mathematica. See the wiki on the heat kernel. $\endgroup$
    – Matthew Cassell
    Commented Feb 27 at 12:32

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