Show by direct substitution that
$ P(x,t) = \frac{1}{\sqrt{4 \pi D t}} \exp \left( - \frac{x^2}{4Dt} \right) $
is a solution to the equation
$ \frac{\partial P}{\partial t} = D \frac{\partial^2 P}{\partial x^2}$
(Please show the full working and reasoning including any annotations that would help a beginner to understand.)
What does it mean by direct substitution? Direct substitution of what into what? What common mathematical techniques am I expected to use here?