3.28 How to set boundary conditions for dsolve or pdsolve?

The Maple syntax for setting initial and boundary conditions is very confusing, as compared to Mathematica, which seems to me to be simpler. So I wrote this to remind me of the syntax each time.

For PDE, assuming dependent variable is \(u(x,t)\) then

Conditions Maple code
\(u(0,t)=0\)  u(0,t)=0
\(\frac {\partial u}{\partial x}=0\) at \(x=0\) D[1](u)(0,t)=0
\(\frac {\partial ^2 u}{\partial x^2}=0\) at \(x=0\) D[1,1](u)(0,t)=0
\(\frac {\partial ^3 u}{\partial x^3}=0\) at \(x=0\) D[1,1,1](u)(0,t)=0
\(\frac {\partial u}{\partial t}=0\) at \(t=0\) D[2](u)(x,0)=0
\(\frac {\partial ^2 u}{\partial t^2}=0\) at \(t=0\) D[2,2](u)(x,0)=0
\(\frac {\partial ^3 u}{\partial t^3}=0\) at \(t=0\) D[2,2,2](u)(x,0)=0

Notice the syntax for the last one above. It is (D[1]@@2)(u)(0,t)=0 and not (D@@2)[1](u)(0,t)=0

For an ODE, assuming dependent variable is \(y(x)\) then the syntax is

Conditions Maple code
\(y(0)=0\)  y(0)=0
\(\frac {dy}{dx}=0\) at \(x=0\) D(y)(0)=0
\(\frac {d^2 y}{d x^2}=0\) at \(x=0\) (D@@2)(y)(0)=0