Write a differential equation in Wolfram Language?

Questions
, ,
1

Hi everybody. I have this function

W = Function[{x, \[Tau]}, \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(n = 1\), \(2\)]\(
\*UnderoverscriptBox[\(\[Sum]\), \(m = 1\), \(2\)]Sin[
\*FractionBox[\(n\ Pi\ x\), \(a\)]] Sin[
\*FractionBox[\(m\ Pi\ y\), \(b\)]] 
\*SuperscriptBox[\(E\), \(\(-I\)\ 
\*SubscriptBox[\(w\), \(n\)] \[Tau]\)]\)\)];

Now I want to write this equation but I don’t know how to do that. Please help me. (i attacked the file)

equation.png

test.nb (2.2 KB)

2

Is the question about formatting for readablility, or about actually writing as input for computation purposes?

3

i want to solve this differential equation

equation.png

where W is

w.png

but i dont know how to do that. can you help me please?
you can consider a=b=1;
n=m=2;
y=2;
D=1;
p=h=1;
?=1;