@Kitonum  Thank you so much. It is really helpful for me.

@Carl Love 

Thank you for your valuable comments.

Is it possible

|cosh(x) | <= exp(x^2/2))

for x is real.

Thanks @Carl Love.

For |cosh(x)| , what is correct assumtion?

@tomleslie 

I am using Mapple 15.

@tomleslie 2741 

Thank you. 

But when I have run this file, few errors are found. You can see in mapple file.

pdeArr.mw

@Carl Love 

Again error is found.pde_solu.mw

@Carl Love 

I want to solve this equation by the following command which is attaching here.

pde_solu.mw